Answer:
Step-by-step explanation:
[tex]R(x)=\frac{x+3}{x-5} \geq 0\\R(x)=0,gives~x+3=0,x=-3\\R(x)>0 ,if~both~numerator ~and~denominator~are~of~same~sign.\\let~x+3>0,x>-3\\and~x-5>0,x>5\\combining \\x>5\\\\again~let~x+3<0,x<-3\\x-5<0,x<5\\combining\\x<-3\\Hence~R(x)\geq 0\\if ~x \in ~[- \infty,-3]U(5,\infty)[/tex]
Pls helppppp,,,,,.....
Answer:
yall do school right now???and i forgot how to do these sorry
Answer:
18 = 2x-14
or, 2x =18+14
or, 2x =32
or, x=32/2
x=16
2(6x-7)=10
or, 12x-14=10
or, 12x=10+14
or, x=24/12
x=2
Plz help me i need this question solution
Answer:
your mom
Step-by-step explanation:
-.p+p⎯.+p Simplify, please.
Answer:
34.5p-2.75
Step-by-step explanation:
First add -0.5p and 12p together which is 11.5p, then add 23p with 11.5p which is 34.5p And -2.75 remains the same
So the answer is 34.5p-2.75
Answer:
34.5p-2.75
Step-by-step explanation:
-0.5p+12p-2.75+23p=34.5p-2.75
plz help me with this question
What is one important role that ocean waters have in heating Earth?
absorb and transport solar energy
transport nutrients and waste
create and emit solar energy
wear away rock and soil
also support me on on ubute SadSpade4679
Answer:
The ocean absorbs heat energy from the sun
Step-by-step explanation:
Yw :)
Answer:
The ocean absorbs heat energy from the sun.
Step-by-step explanation:
help asap!!
Find the length of AB
A. 2.89
B. 33.13
C. 378.63
D. 377.19
Answer:
C
Step-by-step explanation:
[tex] \sin( 5 ^{o} ) = \frac{33}{ab} \\ ab = 378.63[/tex]
Find the first, second, third and fourth order Maclaurin polynomials of f(x) =
arctan(x). Draw the graph of f(x) and the four polynomials on the same
diagram. (Sketch by hand or use software.)
#urgent please give me this answer and help me#
The first, second, third and fourth order Maclaurin polynomials of f(x)=arctan(x) are:
The first order Maclaurin polynomial is f(x)=xThe second order Maclaurin polynomial is also f(x)=xThe third order Maclaurin polynomial is [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]The fourth order Maclaurin polynomial is also [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]You can see the graph on the attached picture.So let's start by finding the first order maclaurin polynomial:
f(x)=f(0)+f'(0)x
so let's find each part of the function:
f(0)=arctan(0)
f(0)=0
now, let's find the first derivative of f(x)
f(x)=arctan(x)
This is a usual derivative so there is a rule we can use here:
[tex]f'(x)=\frac{1}{x^{2}+1}[/tex]
so now we can find f'(0)
[tex]f'(0)=\frac{1}{(0)^{2}+1}[/tex]
f'(0)=1
So we can now complete the first order Maclaurin Polynomial:
f(x)=0+1x
which simplifies to:
f(x)=x
Now let's find the second order polynomial, for which we will need to get the second derivative of the function:
[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}[/tex]
so:
[tex]f'(x)=\frac{1}{x^{2}+1}[/tex]
we can rewrite this derivative as:
[tex]f'(x)=(x^{2}+1)^{-1}[/tex]
and use the chain rule to get:
[tex]f''(x)=-1(x^{2}+1)^{-2}(2x)[/tex]
which simplifies to:
[tex]f''(x)=-\frac{2x}{(x^{2}+1)^{2}}[/tex]
now, we can find f''(0):
[tex]f''(0)=-\frac{2(0)}{((0)^{2}+1)^{2}}[/tex]
which yields:
f''(0)=0
so now we can complete the second order Maclaurin polynomial:
[tex]f(x)=0+1x+\frac{0}{2!}x^{2}[/tex]
which simplifies to:
f(x)=x
Now let's find the third order polynomial, for which we will need to get the third derivative of the function:
[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)}{3!}x^{3}[/tex]
so:
[tex]f''(x)=-\frac{2x}{(x^{2}+1)^{2}}[/tex]
In this case we can use the quotient rule to solve this:
Quotient rule: Whenever you have a function in the form , then it's derivative is:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
in this case:
p=2x
p'=2
[tex]q=(x^{2}+1)^{2}[/tex]
[tex]q'=2(x^{2}+1)(2x)[/tex]
[tex]q'=4x(x^{2}+1)[/tex]
So when using the quotient rule we get:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
[tex]f'''(x)=\frac{(2)(x^{2}+1)^{2}-(2x)(4x)(x^{2}+1)}{((x^{2}+1)^{2})^{2}}[/tex]
which simplifies to:
[tex]f'''(x)=\frac{-2x^{2}-2+8x^{2}}{(x^{2}+1)^{3}}[/tex]
[tex]f'''(x)=\frac{6x^{2}-2}{(x^{2}+1)^{3}}[/tex]
now, we can find f'''(0):
[tex]f'''(0)=\frac{6(0)^{2}-2}{((0)^{2}+1)^{3}}[/tex]
which yields:
f'''(0)=-2
so now we can complete the third order Maclaurin polynomial:
[tex]f(x)=0+1x+\frac{0}{2!}x^{2}-\frac{2}{3!}x^{3}[/tex]
which simplifies to:
[tex]f(x)=x-\frac{1}{3}x^{3}[/tex]
Now let's find the fourth order polynomial, for which we will need to get the fourth derivative of the function:
[tex]f(x)=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)}{3!}x^{3}+\frac{f^{(4)}(0)}{4!}x^{4}[/tex]
so:
[tex]f'''(x)=\frac{6x^{2}-2}{(x^{2}+1)^{3}}[/tex]
In this case we can use the quotient rule to solve this:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
in this case:
[tex]p=6x^{2}-2[/tex]
p'=12x
[tex]q=(x^{2}+1)^{3}[/tex]
[tex]q'=3(x^{2}+1)^{2}(2x)[/tex]
[tex]q'=6x(x^{2}+1)^{2}[/tex]
So when using the quotient rule we get:
[tex]f'(x)=\frac{p'q-pq'}{q^{2}}[/tex]
[tex]f^{4}(x)=\frac{(12x)(x^{2}+1)^{3}-(6x^{2}-2)(6x)(x^{2}+1)^{2}}{((x^{2}+1)^{3})^{2}}[/tex]
which simplifies to:
[tex]f^{4}(x)=\frac{12x^{3}+12x-6x^{3}+12x}{(x^{2}+1)^{4}}[/tex]
[tex]f^{4}(x)=\frac{6x^{3}+24x}{(x^{2}+1)^{4}}[/tex]
now, we can find f^{4}(0):
[tex]f^{4}(x)=\frac{6(0)^{3}+24(0)}{((0)^{2}+1)^{4}}[/tex]
which yields:
[tex]f^{4}(0)=0[/tex]
so now we can complete the fourth order Maclaurin polynomial:
[tex]f(x)=0+1x+\frac{0}{2!}x^{2}-\frac{2}{3!}x^{3}+\frac{0}{4!}x^{4}[/tex]
which simplifies to:
[tex]f(x)=x-\frac{1}{3}x^{3}[/tex]
you can find the graph of the four polynomials in the attached picture.
So the first, second, third and fourth order Maclaurin polynomials of f(x)=arctan(x) are:
The first order Maclaurin polynomial is f(x)=xThe second order Maclaurin polynomial is also f(x)=xThe third order Maclaurin polynomial is [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]The fourth order Maclaurin polynomial is also [tex]f(x)=x-\frac{1}{3}x^{3}[/tex]You can find further information on the following link:
https://brainly.com/question/17440012?referrer=searchResults
Complete the equation describing how x
and y are related.
Х у
y = [? ]x +
07
1 9
2 11
3 13
4 15
5 17
Enter the answer that
belongs in [?]
Answer:
Hello,
Answer 2
Step-by-step explanation:
7=2*0+7
9=2*1+7
11=2*2+7
13=2*3+7
15=2*4+7
17=2*5+7
y=2*x+7
An other way:
[tex]points\ ( 0,7)\ and\ (1,9)\\\\\Delta\ y=9-7=2\\\Delta\ x=1-0=1\\\\\\y-7=(x-0)*2\\\\y=2x+7\\[/tex]
The complete equation is [tex]y = 2x+7[/tex].
What is equation?An equation is a condition on a variable such that two expressions in the variable should have equal value.
What is substitution?Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.
According to the question.
We have a table which shows the relation between x and y.
Let the missing term be a and b.
The the given equation becomes
[tex]y = ax + b[/tex]
For finding the value of a and b.
Substitute x = 0 and y = 7 in equation y = ax + b.
[tex]\implies 7 = a(0) + b\\\implies b = 7[/tex]
Again, substitute x = 1 and y = 9 in the equation y = ax+ b
[tex]\implies 9 = a(1) +b\\\implies 9 = a + 7\\\implies a = 2[/tex]
substitute the value of a and b in the equation y = ax + b.
[tex]\implies y = 2x+ 7[/tex]
Therefore, the complete equation is [tex]y = 2x+7[/tex].
Find out more information about equation and substitution here:
https://brainly.com/question/2581775
#SPJ2
The salt content in snack bags of pretzels is Normally distributed, with a mean of 180 mg and a standard deviation of 15 mg. Eighty four percent of bags have a salt content higher than which value?
Find the z-table here.
165.2 mg
179.2 mg
187.0 mg
194.9 mg
I think its (A), 165.2mg
Answer: Yes you are correct. The answer is choice A
============================================================
Explanation:
If you used the z-table, you should find that P(Z < 1) = 0.84 approximately.
So by symmetry, P(Z > -1) = 0.84 approximately as well.
We'll convert the z score z = -1 into its corresponding x score
z = (x-mu)/sigma
-1 = (x-180)/15
-15 = x-180
x-180 = -15
x = -15+180
x = 165
We don't land on any of the answer choices listed, but we get fairly close to 165.2, which is choice A. So you are correct.
I have a feeling that the table you have is probably more accurate than the one I'm using, so it's possible that you'd land exactly on 165.2 when following the steps above.
Answer:
194.9
Step-by-step explanation:
ON EDG
After running 3/4 of a mile tess has only run 1/3 how long is the race in miles but I want to know how you did it
The lifetimes of light bulbs of a particular type are normally distributed with a mean of 350 hours and a standard deviation of 6 hours. What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
Answer:
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?
By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.
The sum of a number x and
eleven
Answer:
what is the sum.
Step-by-step explanation:
Take the sum - 11 =x
What is the common difference for this arithmetic sequence?
-6,-1,4,9,14,...
A. 6
B. 4
C. 5
D. 3
SUBMIT
Answer:
5 is the answer to your question
Step-by-step explanation:
the numbers are increasing by +5
What is the equation of the line that passes through (4,3) and (2, -1)?
y = 4x -13
y = 6x+4
y = 2x-5
y = 1/2 x -2
Answer:
y=2x-5
Step-by-step explanation:
By using two-points form:
y-y1/y2-y1=x-x1/x2-x1
p(x1,y1)=(4,3)
p(x2,y2)=(2,-1)
Subtitute points in formula:
y-3/-1-3=x-4/2-4
y-3/-4=x-4/-2
y-3/-2=x-4/-1
1(y-3)=2(x-4)
y-3=2x-8
y=2x-8+3
y=2x-5
Note:if you need to ask any question please let me know.
Smart phone: Among 239 cell phone owners aged 18-24 surveyed, 103 said their phone was an Android phone. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone. Round the answer to at least three decimal places. The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is .
Answer:
The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.
Step-by-step explanation:
The point estimate is the sample proportion.
Sample proportion:
103 out of 249, so:
[tex]p = \frac{103}{249} = 0.4137[/tex]
The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.
One angle of a triangle is equal to the sum of the remaining angles. If the ratio of measures of the ren
is 2:1, find the measures of the three angles of the triangle.
9514 1404 393
Answer:
90°, 60°, 30°
Step-by-step explanation:
The remaining angles have a ratio of 2:1, so total 3 "ratio units". The first angle is equal to that sum: 3 ratio units, so all of the angles together total 3+2+1 = 6 ratio units. The total of angles is 180°, so each ratio unit is 180°/6 = 30°.
The first angle is 3 ratio units, or 90°.
The second angle is 2 ratio units, or 60°.
The third angle is half that, or 30°.
The three angles are 90°, 60°, 30°.
Geometry please help me need help I don’t know how to do it
Answer:
A'(0,-8) B'(5,-7) C'(3,0) D'(2,-5)
A''(0,8) B''(-5,7) C''(-3,0) D''(-2,5)
Step-by-step explanation:
first everything is shifted down 8 units (x,y-8), so we get A'(0,-8) B'(5,-7) C'(3,0) D'(2,-5)
then you multiply by -1 A''(0,8) B''(-5,7) C''(-3,0) D''(-2,5)
what is the mean of this graph?
Answer:
Step-by-step explanation:
Mean: sum of terms/ number of terms
4 + 2 + 3 + 1 + 1 + 5 = 16
Numbr of terms = 6
16/6 = 2.66
Answered by g a u t h m a th
Answer:
2 2/3
Step-by-step explanation:
The mean is the average of the values
The values on the graph are 4, 2, 3, 1, 1, and 5
Average is sum/number of values
4+2+3+1+1+5=16
16/6=2 2/3
Find the values for x and y using the diagram below. Explain what geometric relationships you used to solve the problem.
You DO NOT have to write a proof. An example would be "linear pair" or "right angles= 90◦
".
Answer:
2x, a linear pair
Step-by-step explanation:
2/5x/3/4 = 7/4 = 1 3/4
596 is divisible by 2?
a.yes
b.no
Answer:
It's yes
Step-by-step explanation:
Answer:
yep
Step-by-step explanation:
number is even, so it can be evenly divided by 2. :)
PLEASE HELP!!! ITS DUE TONIGHT!!!!!
YOUR ASSIGNMENT: Difference of 10
Erik and Nita are playing a game with numbers. In the game, they each think of a random number from 0 to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins. Use the information in the interactive and what you know about absolute value inequalities to better understand the game.
Your Player
1. Choose your player, and record the number chosen by the other player. (2 points: 1 point for each answer)
a. Which player did you select?
b. What number did the other player pick?
Modeling Ways to Win
2. Should you use an equation or an inequality to represent the ways your player can win? Why? (2 points: 1 point for an answer, 1 point for an explanation)
3. Imagine that Erik chose a 4 and Nita chose a 12. Would the winner be different if Nita chose the 4 and Erik chose the 12? (2 points: 1 point for an answer, 1 point for an explanation)
4. Is it appropriate to use an absolute value inequality to represent how a player wins this game? Why? (2 points: 1 point for an answer, 1 point for an explanation)
5. If your player is Erik, write an inequality that shows all of the ways that Erik will win if Nita chooses 7. If your player is Nita, write an inequality that shows all of the ways that Nita will win if Erik chooses 17.
Be sure to define your variable. (3 points: 1 point for defining the variable, 2 points for the correct inequality)
6. In order to graph your solutions, solve for the variable. Be sure to show your work. (2 points)
7. Sketch a graph of your solutions. (2 points: 1 point for endpoints, 1 point for the correct region)
Forming a Strategy and a New Rule
8. What is the range of numbers that will win the game for your player?
If your player is Erik, assume that Nita chooses 7.
If your player is Nita, assume that Erik chooses 17.
(Hint: Remember that Erik and Nita can choose only numbers from 0 to 20, inclusive.) (2 points)
9. Graph all the possible numbers that either player could pick. Compare this graph with your answer in question 8.
If your player is Erik, and Nita chooses 7, does Erik have a good chance of winning?
If your player is Nita, and Erik chooses 17, does Nita have a good chance of winning?
Explain your answer. (3 points: 1 point for the correct graph, 2 points for the explanation)
Answer:
it is too long send me link of it
Answer: Choose your player, and record the number chosen by the other player. (2 points: 1 point for each answer) a. Which player did you select? Erik, assume that Nita chooses 7. b. What number did the other player pick? 17
2. Should you use an equation or an inequality to represent the ways your player can
win? Why? (2 points: 1 point for an answer, 1 point for an explanation)
An algebraic statement that represents all the ways Eric will wins is
where
be the number that Eric thi
3. Imagine that Erik chose a 4 and Nita chose a 12. Would the winner be different if
Nita chose the 4 and Erik chose the 12? (2 points: 1 point for an answer, 1 point for
an explanation)
no because both nita and eric won. eric with a number less than than 10
and nita with a number more than 10.
4. Is it appropriate to use an absolute value inequality to represent how a player wins
this game? Why? (2 points: 1 point for an answer, 1 point for an explanation)
they win it remains positive the negative will be losses which will be changed due to
absolute value
5. If your player is Erik, write an inequality that shows all of the ways that Erik will win
if Nita chooses 7. If your player is Nita, write an inequality that shows all of the ways
that Nita will win if Erik chooses 17.
Be sure to define your variable. (3 points: 1 point for defining the variable, 2 points for
the correct inequality)
Step-by-step explanation:
factorise completely 4x^(2 )(x + 1) - 6x (x+1)
Answer:
[tex] {4x}^{2} (x + 1) - 6x(x + 1) \\ = (x + 1)(4 {x}^{2} - 6 x ) \\ = (x + 1)(2x)(2x - 3)[/tex]
explanation:
first choose the common factor by observation, it is (x + 1):
factorise it out:
= (x + 1)(4x² - 6x)
by observation in (4x² - 6x), common factor is 2x.
Factorise 2x out:
= (x + 1)[2x(2x - 3)]
Answer:
(4x2-6x) (x+1)
now common factor is (x+1) ,so,(4x2-6x) (x+1)
What is the area of this figure?
Answer:
22
Step-by-step explanation:
(5x2) + (3x2) + (3x2)
22 square units
Answer from Gauthmath
A building is 1 ft from an 8-ft fence that
surrounds the property. A worker wants
to wash a window in the building 11 ft
from the ground. He plans to place a
ladder over the fence so it rests against
the building. (See the figure.) He
decides he should place the ladder 8 ft
from the fence for stability. To the
nearest tenth of a foot, how long a
ladder will he need?
Answer:
This question is mainly about pythagorean theorm as if we just analyse this question we see the information given to us are
The height of the building = 11 ft The distance in between the fence and the building = 1 ftThe distance of ladder from the fence = 8 ftNow it is said to find out the length of ladder as because the ladder is resting against the buiding so it will generally form an acute angle with the ground and as we can take the ladder to be as the hypotenuse of a right angled triangle in which the length of the perpendicular building forms one of the leg and the distance of the building from the point where the ladder is kept is said to be another leg
Now we get the measure of the vertical leg = height of the buiding = 11 ft
and another leg = distance in between the fence and the point on which the ladder is kept + the distance in between the fence and building
= (8+1)ft =9ft
Now we know hypotenuse = √base^2+√height^2
= √9^2+√11^2
= √81+√121
= √ 202
= 14.21 ft
Therefore the length of the ladder = 14.21 ft
Hope it helps you
The length of the ladder should be 11.1 feet long.
Let's denote the length of the ladder as L.
According to the given information:
The distance from the building to the fence = 1 ft.
The height of the window = 11 ft.
The distance from the ladder to the fence = 8 ft.
Using the Pythagorean theorem, we can set up the equation:
[tex]L^2 = (1^2) + (11^2)[/tex]
Simplifying:
[tex]L^2 = 1 + 121[/tex]
[tex]L^2 = 122[/tex]
Taking the square root of both sides:
[tex]L = \sqrt{122}[/tex]
[tex]L = 11.05 ft[/tex]
Therefore, the worker will need a ladder approximately 11.1 feet long.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ4
One year, Alex bought an antique car for his birthday. During the first year he owned it, the
value of the car gained 10%. During the second year, the value of the car gained another
15% from the previous year. If the value of the car is now $37,950.00, how much did Alex
originally pay for his car?
Answer:
28462.5
Step-by-step explanation:
During the first year it gained 10% and during his second year he gained 15% so you first add those and you get 25%.
Then you multiply 25% with 37,950.
25/100 * 37950 = 948,750/100
= 9487.5
To get the original amount you subtract 9487.5 from 37,950
37,950 - 9487.5 = 28462.5
So the original amount was 28462.5
Find the length of AC again
Answer:
B
Step-by-step explanation:
side Ac is the opposite of angle B, therefore use the sin ratio to find ac since the hypotenuse is also given
sin B=opposite/hypotenuse
sin 27=ac/15
ac=sin27×15
=6.81
I hope this helps
Answer:
AC = 6.81
Step-by-step explanation:
∠BAC = 90° - 27° = 63°
Cos 63° =[tex]\frac{AC}{AB}[/tex] = 0.454
AC = cos 63° * AB = 0,454 * 15 = 6.81
The minimum point of the graph y = 2x^2 + 2x +1 is located at:
Answer:
A
Step-by-step explanation:
By completing the square, y = 2x^2 + 2x +1 will be y=2(x+1/2)^2+(1/2) the minimum point is the vertex of the parabola which is (-1/2, 1/2)
From the picture, two cylindrical glasses of the same capacity. Find the diameter length (X) of a small glass of water.
8
12
14
10
Answer:
12
Step-by-step explanation:
πr²h=πr²h
π(4.5)²*10=π(x/2)²4.9
I need help completing this answer are you available
Answer:
Step-by-step explanation:
Solving Equations by Dividing 2) 9x= -135 Solve for x. 0 -144 O 126 O 15 0 -15
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{9x = -135}}[/tex]
[tex]\huge\boxed{\text{DIVIDE 9 to BOTH SIDES}}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{9x}{9}= \dfrac{-135}{9}}}[/tex]
[tex]\huge\boxed{\mathsf{\bullet \ CANCEL: \dfrac{9}{9}\ because\ it \ gives\ you\ 1}}[/tex]
[tex]\huge\boxed{\bullet\ \mathsf{KEEP: \dfrac{-135}{9}\ because\ it\ helps\ solve \ for}}\\\huge\boxed{\mathsf{the\ x-value}}[/tex]
[tex]\huge\boxed{\mathsf{x = \dfrac{-135}{9}}}\\\\\huge\boxed{\mathsf{\dfrac{-135}{9}= x}}}[/tex]
[tex]\huge\boxed{Simplify \ it\uparrow}[/tex]
[tex]\huge\boxed{\mathsf{x = \bf -15}}[/tex]
[tex]\huge\boxed{\textsf{Therefore, your answer is: Option D. -15 }}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
What is the complete factorization of the polynomial below?
x3 + 4x2 + 16x + 64
Answer: (x+4) ( x-4i)(x+4i)
Discussion:
Factor the polynomial:
x^3+4x^2+16x+64 = (x +4 ) ( x^2 + 16) (*)
Factor x^2 +1 6 over the complex numbers:
x^2 + 16 = (x -4i)(x+4i) (**)
Combing (*) and (**) gives the full factorization
(x+4) ( x-4i)(x+4i)
