How to synthetically divide polynomials.
Answer:
Write down the problem. For this example, you will be dividing x3 + 2x2 - 4x + 8 by x + 2. Write the first polynomial equation, the dividend, in the numerator and write the second equation, the divisor, in the denominator.
Reverse the sign of the constant in the divisor. The constant in the divisor, x + 2, is positive 2, so reversing the sign of the constant would give you -2.
Since the opposite of the constant term is -2, we put the -2 inside a box. A common mistake is to put a 2 inside the box, watch out here.
Write all of the coefficients of the dividend inside the division symbol. [2] Write the terms from left to right, just as they appear. It should look like this: -2| 1 2 -4 8.
Bring down the first coefficient. Bring down the first coefficient, 1, below itself. It should look like this:
-2| 1 2 -4 8
↓
1
Multiply the first coefficient by the divisor and place it under the second coefficient.[3] Simply multiply 1 by -2 to get -2 and write this product under the second term, 2. Here's how it would look:
-2| 1 2 -4 8
-2
1
Add the second coefficient and the product and write the answer below the product. Now take the second coefficient, 2, and add it to -2. The result is 0. Write this result below the two numbers, just as you would in long division. Here's how it would look:
-2| 1 2 -4 8
-2
1 0
Multiply this sum by the divisor and place the result under the third coefficient. Now take the sum, 0, and multiply it by the divisor, -2. The result is 0. Place this number below 4, the third coefficient. It should look like this:
-2| 1 2 -4 8
-2 0
1
Add the product and the third coefficient and write the result under the product. Add 0 and -4 to get -4 and write this answer below the 0. Here's how it would look:
-2| 1 2 -4 8
-2 0
1 0 -4
Multiply this number by the divisor, write it under the last coefficient, and add it to the coefficient. Now, multiply -4 by -2 to get 8, write this answer under the fourth coefficient, 8, and add this answer to the fourth coefficient. 8 + 8 = 16, so this is your remainder. Write this number below the product. Here's how it would look:
-2| 1 2 -4 8
-2 0 8
1 0 -4 |16
Place each of the new coefficients next to a variable of one less power than their original corresponding variables. In this case, the first sum, 1, is placed next to an x to the second power (one less than three). The second sum, 0, is placed next to an x, but the result is zero, so you can remove this term. And the third coefficient, -4, becomes a constant, a number without a variable, since the original variable was x. You can write an R next to the 16, because that is the remainder. Here's how it would look:
-2| 1 2 -4 8
-2 0 8
1 0 -4 |16
x2 + 0x - 4 R 16
x2 - 4 R16
Write the final answer. The final answer is the new polynomial, x2 - 4, plus the remainder, 16, over the original divisor, x + 2. Here's how it would look: x2 - 4 +16/(x +2).
Step-by-step explanation:
That was quite long, but those are the steps to synthetically divide polynomials.
Check the number or numbers that are in the solution set of the equation
below.
7x > 42
A. 14
B. 5
C.35
D. 6
E. 12
F9
Answer:
A, C, E, F
Step-by-step explanation:
when you multiply the numbers with 7 the answer is greater than 42
Does anyone want to play prodigy with me? if so meet at Town Square in Lamplight Town in Sapphire World. I'm Serenity Nearshadow in that game. PLEASE!
Answer:
why did you need to play with you are you board of playing then stop playing game
Solve the slope for the table.
Answer:
5
Step-by-step explanation:
Change in Y / Change in X = Slope
5/1 = 5
300
O
3) What is the value of x?
69'
7090
7100
3D
Answer:
71°
Step-by-step explanation:
exterior angle = sum of two opposite interior angle
142°=2x°
x°=142°/2
x°=71°.
hope this helps you.
y = 147° ( Vertically opposite angles)
[tex]y + x + x = 180° \\ 147 + 2x = 180° \\ 2x = 180 - 147 \\ 2x = 33 \\ x = \frac{33}{2} \\ x = 16.5[/tex]
Daniella has 130 baseball cards. She buys new cards to her collection every month. Which arithmetic sequence describes the number of cards in her collection?
Answer:
a1=130;an=an−1+10
Step-by-step explanation:
The answer is the third one.
She starts with 130
a1 = 130
She adds 10 every month.
So you take the number she had last month (represented by a_n-1) and adds 10.
Answer
a1 = 130
an = an_1 + 10
C
Emma but two identical bottles of shampoo. She uses 3/8 of one of them at home, and uses 7/10 of all of the remaining while she’s on Hollidays. In total, how much shampoo remains?
Answer:
37/40
Step-by-step explanation:
3/8 7/10
80/40 - 15/40 - 28/40 = 37/40
two whole shampoo - uses at home - uses on holiday = left
Simplify the expression.
I NEED HELP PLEASE!!!
Answer:
-27/64p^3
Tell me if you want a step by step. :)
Зx — 6 = 3х – ?
-6
6
З
-3
0
Answer:
3x--666667666666666666666666666666
A manufacturer produces cell phone she estimates that by selling them for x dollars she will be able to sell them for 285 minus 2X each week determine what the maximum revenue will be round your answer to two decimal places
Answer:
38.30
Step-by-step explanation:
because 230 -6x=0
(4)/(12)= ()/(3) what makes this equivalent
Answer:
1/3
Step-by-step explanation:
4/12 divide by 4 to the top and bottom you get 1/3
[tex]\dfrac 4{12} = \dfrac{ 4 \times \tfrac 14 }{12 \times \tfrac 14} = \dfrac 13\\\\\\\\\text{Hence the answer is 1}[/tex]
5^-15 rewritten using a positive exponent.
Answer: 1/5 to the power of 15
Find the missing side.
09
9.5
10
C
7 cm
10.6
8 cm
HELP PLEASE
Answer:a
Step-by-step explanation:
i know
PLS HELP ASAP ILL GIVE BRAINLKEST
Answer:
4th option
Step-by-step explanation:
solve the equation.
[tex]\sqrt{x(x+2)} = 0[/tex]
[tex]\sqrt{x(x+2)} = 0 <=> x(x+2)=0\\<=> x=0 /or/ x+2=0 <=> x=0 /or/ x=-2[/tex]
ok done. Thank to me :>
3/10y - 2/5 i need to find the coefficient and i dont know how
[tex] \frac{3}{10y} - \frac{2}{5} = \frac{3 - 4y}{10y} [/tex]
can someone help me plsss
Answer:
c=23/24
Step-by-step explanation:
c+3/8=1/1/3
c+3/8=4/3
c+9/24=32/24
c=32/24-9/24
=23/24
Monica deposits $300 into a savings account that pays a simple interest rate of 3.9%. Paul deposits 400$ into a savings account that pays a simple interest rate of 3.2%. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.
Answer:
For Monica : Principle = $300 rate : 3.4% time 1 yr
Simple interest = Prt/100 = 300*3.4*1/100 = 1020/100= $ 10.2
For Paul : Principle = $400 rate : 2.8% time 1 yr
Simple interest = Prt/100 = 400*2.8*1/100 = 1120/100= $ 11.2
Step-by-step explanation:
You have a recipe that indicates to use 6 parts of sugar for every 5 parts of flour. You use 24 cups of sugar. How much flour do you need?
Sean wants to spend (example) $100 on clothing and he wants to purchase 6 additional items for his wardrobe. Each pair of pants costs $20 and each shirt costs $15.
a. What is the system of equations that represents this situation?
b. Can he buy 2 pair of pants and 4 shirts?
c. Show the solution graphically.
Please answer quickly!
A: I do not understand.
B: Yes
C: 2 pair pants is $40. 4 pair shirts is $60. $60 + $40 = $100
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
8x + 6y = -54
Answer:
y = - 4/3x - 9
Step-by-step explanation:
Answer:
[tex]y = -\frac{4}{3}x - 9[/tex]
Step-by-step explanation:
The standard form of linear equation is: Ax + By = C, where A, B, and C are integers; A and B ≠ 0, and A is a non-negative integer.
Given the linear equation in standard form, 8x + 6y = -54, we can transform this equation into its slope-intercept form, y = mx + b.
First, subtract 8x from both sides:
8x + 6y = - 54
8x - 8x + 6y = - 8x - 54
6y = -8x - 54
Divide both sides by 6 to isolate y:
[tex]\frac{6y}{6} = \frac{-8x - 54}{6}[/tex]
[tex]y = -\frac{4}{3}x - 9[/tex] ⇒ This is the slope-intercept form where the slope, m = [tex]- \frac{4}{3}[/tex], and the y-intercept, b = -9.
A 150-pound person uses 4.8 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 250
calories?
Answer:
52.083
Step-by-step explanation:
1 min = 4.8 calories
? min=250calories
at the age speed
250/4.8 calories
=52.083min
Help me please I’m bad at slopes
Answer Please will give brainliest.
Step-by-step explanation:
blue is natural: 1, 4, 0, 2 and root of 25.
green is whole: -9 and -15.
yellow is rational: 2/3
orange is irrational: pi and root of 15.
white is real numbers.
don't know about that purple one.
PLEASE HELP!! The figure below shows a line graph and two shaded triangles that are similar:
A line is shown on a coordinate grid. The x axis values are from negative 10 to positive 10 in increments of 2 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 6, negative 3, and 0, 0, and 6, 3. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled O to 4, 2 labeled A, one leg is from 0, 0 to 4,0, and the second leg is from 4,0 to 4, 2. Another shaded right triangle is formed with the hypotenuse is from 4, 2 to 6, 3 labeled B, one leg is from 4, 2 to 6, 2, and the second leg is from 6, 2 to 6, 3.
Which statement about the slope of the line is true?
It is fraction 1 over 2 throughout the line.
It is 2 throughout the line.
The slope from point O to point A is fraction 1 over 2 times the slope of the line from point A to point B.
The slope from point O to point A is 2 times the slope of the line from point A to point B.
The slope of the line of the graph is given by the ratio of the change in y-
coordinates to the change in the x-coordinates of the line.
The statement that is true about the slope of the line is; it is [tex]\dfrac{1}{2}[/tex] throughout
the line.
Reasons:
The given parameter are;
The ordered pair through which the line passes = (-6, -3), and (0, 0) and (6, 3)
Points on the hypotenuse of the shaded right triangle = O(0, 0), and A(4, 2)
Points on the leg of the right triangle = (0, 0) to (4, 0)
Points on the second leg of the right triangle = (4, 0) to (4, 2)
Second right triangle;
Points on the hypotenuse = A(4, 2) to B(6, 3)
One leg of the right triangle extends from (4, 2) to (6, 2)
Second leg extends from (6, 2) to (6, 3)
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\mathrm{Slope, \, of \ first \ triangle, \, m} =\dfrac{2-0}{4-0} = \dfrac{1}{2}[/tex]
[tex]x^{2} \mathrm{Slope, \, of \ second \ triangle, \, m} =\dfrac{3-2}{6-4} = \mathbf{\dfrac{1}{2}}[/tex]
Therefore;
The slope is [tex]\dfrac{1}{2}[/tex] throughout the line
Learn more here:
https://brainly.com/question/24861248
$61.60 for parts and labor rate is $30.00 per hour total cost 136.60 how many hours will the job take? Write an equation and explain how you used it to find the number of hours the job will take.
Answer:
(136.60 - 61.60) / 30 = 2.5 hours
Step-by-step explanation:
First, subtract the cost of parts from the total: 136.60 - 61.60 = 75
Now you have the total labor cost. Divide by the hourly rate: 75 / 30 = 2.5
Find the perimeter, in feet, of the rhombus.
32 feet
60 feet
34 feet
68 feet
Answer:
68ftStep-by-step explanation:
The formula of a perimeter of a rhombus:
P = 4a
a - length of side
We have a = 17ft
P = 4 · 17ft = 68ft
Please help me The point D,E,F and G all lie on the same segment, in that order, such that ratio of DE:EF:FG is equal to 4:1:4. If DG=36, find EG
Answer:
4+1+4+g=36
g=27
dg=32
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
DE : EF : FG = 4 : 1 : 4
DG = 36
DG = DE + EF + FG
-> 4x + x + 4x = 36
9x = 36
x = 4
so EG = EF + FG
= x + 4x
= 5x
= 20
helppp,no links or spam
Answer: 6.45 x 10^10
Step-by-step explanation:
Because 10^5 and 10^4 both have 10, we can add the exponents to get 10^9.
Multiplying 7.5 and 8.6 gets you
7.5 * 8.6 = 64.5
We can move the decimal up a place to get 6.45 and add another power to 10^9 to get 10^10
Your final answer should be 6.45 x 10^10
Answer:
C 6.45x 10 to the power of 10
Step-by-step explanation:
10 to the power of 5 is 100,000. 7.5x100,000 is 750,000.
10 to the power of 4 is 10,000.
10,000x8.6 is 86k
now we do 750,000x86,000 which is 64,500,000,000
10 to the power of 10 is 10 billion times 6.45 is 64,500,000,000
5.
Identify the vertex of the parabola.
A. (6, 3)
B. (3, 0)
C. (4, -1)
D. (5, 0)
Answer:
B. (3, 0)
Step-by-step explanation:
It's B. (3,0) because it's on the line of 3 and 0 aka x axis