Find all of the rational zeros of the function. ​f(​x)=x ​4 −3x ​3 −6x ​2 +6x+8 ​

Answers

Answer 1

Answer:

The "possible" rational zeros are:

±

1

,

±

2

,

±

4

,

±

8

The actual zeros are:

1

,

4

,

±

2

Explanation:

f

(

x

)

=

x

4

3

x

3

6

x

2

+

6

x

+

8

By the rational root theorem, any rational zeros of

f

(

x

)

are expressible in the form

p

q

for integers

p

,

q

with

p

a divisor of the constant term

8

and

q

a divisor of the coefficient

1

of the leading term.

That means that the only possible rational zeros are:

±

1

,

±

2

,

±

4

,

±

8

We find:

f

(

1

)

=

1

+

3

6

6

+

8

=

0

So

x

=

1

is a zero and

(

x

+

1

)

a factor:

x

4

3

x

3

6

x

2

+

6

x

+

8

=

(

x

+

1

)

(

x

3

4

x

2

2

x

+

8

)

Notice that the ratio between the first and second terms of the remaining cubic is the same as that between the third and fourth terms. So this cubic will factor by grouping:

x

3

4

x

2

2

x

+

8

=

(

x

3

4

x

2

)

(

2

x

8

)

x

3

4

x

2

2

x

+

8

=

x

2

(

x

4

)

2

(

x

4

)

x

3

4

x

2

2

x

+

8

=

(

x

2

2

)

(

x

4

)

Finally we can factor the quadratic as a difference of squares:

x

2

2

=

x

2

(

2

)

2

=

(

x

2

)

(

x

+

2

)

So the zeros are:

1

,

4

,

±

2


Related Questions

spilled $40 into the ratio of 3:7

Answers

Answer:

$12/$28

Step-by-step explanation:

Let x and y represent the two amounts of money adding up to $40.

Assume that x is the smaller amount.  Then:

 x        3

----- = -----    Remembering that x + y = $40, we get x = $40 - y

 y        7

amd sp we have

 $40 - y          3

-------------- = ------   which, after cross-multiplication, is $280 - $7y = 3y

       y             7

Simplifying this, we get $280 = 10 y, so that y must be $28.  If y = $28, x must be $40 - $28, or $12.

                                                                             $12

Then $40, split in the ratio 3/7, is the ratio ----------------

                                                                            $28

Check:  Note that $12 + $28 = $40, as required, and that $12/$28 = 3/7.

6457/25 using partial products

Set up using the same way please.

Answers

Answer: 6457/25=258.28

Step-by-step explanation:

Answer:

258.28  Hope this helps! Please mark brainliest it means a lot to me

Step-by-step explanation:

Th=0

H=2

T=5

0=8

tenth=2

hundredth=8

You could get the answer by doing long division/standard algorithm

Which expression simplifies to 5√3?

Answers

Answer:

C.

[tex] \sqrt{75} [/tex]

Step-by-step explanation:

You can just enter it in the calculator to see which is equal to

[tex]5 \sqrt{3} [/tex]

solve the equation 5(3x-1)=4(3x-2)

Answers

Answer:

x=-1

Step-by-step explanation:

15x-5=12x-8 Simplify Parentheses

3x=-3 Isolate the variable

x=-1 Divide by 3 on both sides

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

Our equation is

[tex]5\left(3x-1\right)=4\left(3x-2\right)[/tex]

First, we distribute

Now we have

[tex]15x-5=12x-8[/tex]

Subtract [tex]12x[/tex] from both sides

[tex]3x-5=-8[/tex]

add [tex]5[/tex] to both sides

[tex]3x=-3\\[/tex]

Divide both sides by 3

[tex]x=-1[/tex]

Brainliest please

make v the subject of the formula t=4v+3

Answers

Step-by-step explanation:

t=4v+3

t-3=4v

(t-3)/4=v

hope this helps you.

if "-3(y-10=9" what is the value of y-12

Answers

Answer:

the correct answer is -5 since y=7

18917-8- 1819-7 18918

4d=12 solve for the variable

Answers

Answer; d=3
Let me know if you need an explanation!

Given the complementary angle of y is 43º. Find the supplementary angle of y​

Answers

Step-by-step explanation:

complementary = adds up to 90 degrees.

supplementary = adds up to 180 degrees.

the complementary angle of y is 43 degrees.

so, y = 90 - 43 = 47 degrees.

the supplementary angle of y = 47 is

180 - 47 = 133 degrees

Hello!

Given the complementary angle of y is 43º.

90 - 43 => 47°

Find the supplementary angle of y​

180-43 => 137°

Somebody please help

Answers

Answer:

c/  y=20x

Step-by-step explanation:

You have 2\3 of a pizza left from yesterday. You divide it into 4 equal pieces. What fraction of the pizza is each piece?​

Answers

Answer:  1/6

====================================================

Explanation:

Let's say for example this pizza had 6 slices to start with. Two-thirds of this is (2/3)*12 = 4 slices. So you have 4 slices left over from yesterday. Then let's say you hand one slice to each of your four friends. Each friend would have 1/6 of the original pizza.

1\4-2\5
plese help and thank
you

Answers

Answer:

3/20

Step-by-step explanation:

3/20 I sure, Just trying this one


Calculate measures of central tendency and
dispersion for the following:

Find the mean, median, midrange, mode, range, standard deviation and Quartile graph

Data: 54, 92, 101, 83, 45, 102, 99,76, 79, 85, 90, 100,
98, 71, 65, 63, 90, 88, 70, 60, 90, 58,81

Answers

Answer:

The mean is 80, the median is 83, and the mode is 90

Step-by-step explanation:


Which postulate or theorem proves that these two triangles are
congruent?
O ASA Congruence Postulate
O AAS Congruence Theorem
O HL Congruence Theorem
O SAS Congruence Postulateo

Answers

Answer: O AAS Congruence Theorem is your answer

Step-by-step explanation:   plz give brainliest

How many rows would be returned from a cross join of tables A and B, if A contains 8 rows and B contains 18

Answers

The number of rows that would be returned from the cross join of tables A and B is 144 rows.

The cross join of table A and table B is the cartesian product of A and B.

Since table A = 8 rows and table B = 18 rows, the cartesian product of the rows is 8 × 18 = 144 rows.

So, the number of rows that would be returned from the cross join of tables A and B is 144 rows.

Learn more about cross join here:

https://brainly.com/question/24263570

what is the x intercept

Answers

Answer:

The answer is B

0.125 ultiply by 1000

Answers

Answer:

125 is answer .........:)

plz help me fast Simplify t12/t6

Answers

Answer:

t^6

Step-by-step explanation:

when dividing exponents, you subtract (refer to exponent rule)

t^12 - t^6 = t^6

Select the correct answer.
What is the vertex of the function f(x) = |x + 7| − 3?

Answers

the vertex is at (-7,-3)

Find the perimeter. Simplify your answer.

Answers

Answer:

4

Step-by-step explanation:

yeah-ya........ right?

The perimeter of the triangle is 2(12c - 7).

What is a triangle?

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees. The perimeter of a triangle is the sum of the side lengths.

What is the perimeter of the triangle?

Perimeter = 7c - 5 + 7c - 5 + 10c - 4

24c - 14

2(12c - 7)

To learn more about a triangle, please check: https://brainly.com/question/9329354

If a triangle has a base of 6 feet and a height of 5 feet, what is the area?

Answers

Answer:

15 square feet

Step-by-step explanation:

a = (1/2)bh

a = (1/2) * 6 * 5

a = 3 * 5

a = 15

15 square feet

Need help really quick look at the picture thank you soooooooo,, muchh

Answers

Answer:

The answer would be -7/12

Step-by-step explanation:

Use math.way itll help you tremendously :)

100-3x6+5-4= 63? help me its GEMDAS

Answers

Answer:

it's 86

Step-by-step explanation:

100-3x6+5-4

100-15+5-4

85+5-4

90-4

86

In the partial sequence …, 987, N, 2584, 4181, …, each new term is the sum of the two previous terms. Find the whole number value of N.

Answers

Answer: 2584

Step-by-step explanation:

We can find N with 2584 and 4181.

4181 - 2584

= 1597

We can also check our answer by adding 1597 and 987

1597 + 987

= 2584

A sequence can be arithmetic, geometric or neither.

The value of N is 1597

The partial sequence is given as:

.... 987, N, 2584, 4181......

From the question, the current term is the sum of two previous terms.

This means that:

[tex]\mathbf{987 + N = 2584}[/tex] and

[tex]\mathbf{N + 2584 = 4181}[/tex]

Make N the subject in both equations

[tex]\mathbf{N = 2584 - 987}[/tex]

and

[tex]\mathbf{N = 4181 - 2584 }[/tex]

So, we have:

[tex]\mathbf{N = 1597}[/tex]

and

[tex]\mathbf{N = 1597}[/tex]

Hence, the value of N is 1597

Read more about partial sequence at:

https://brainly.com/question/12914852

I need help quickly

Answers

the answer is 6 (x- 5)= 36

What is the area of this tile?

Answers

Answer:

Area: 9 in.²

Step-by-step explanation:

Area of square: side²

=> Area of Square tile: 3²

=> 9 in.²

Hoped this helped.

Answer:

9

Step-by-step explanation:

To find the area of a square, multiply both sides.

3*3=9

Find the equation of the line that passes through (3,1) and is parallel to y = 3 − 2 x . Leave your answer in the form y = m x + c

Answers

Answer:

y=3-2x

Step-by-step explanation:

Parallel to y = 3 − 2 x => y=c-2x

Through (3,1) => 1=c-2(1) <=> c=3

Line is y=3-2x

how do you simplify 2.7 x 6

Answers

Answer:

16.2

Step-by-step explanation:

|2x + 6| = 16
plsss helppp

Answers

Answer:

x = 5

Step-by-step explanation:

|2x + 6| = 16

=> 2x + 6 = 16

=> 2x = 16 - 6

=> 2x = 10

=> x = 5

Hoped this helped.

X=5
2x +6 = 16
-6 -6
2x = 10
/2 /2
X=5

plss help, it’s pretty easy tho

Answers

Answer:

B

Step-by-step explanation:

Mindy can a drive a total of 375 miles on a full tank of gas, which is 25 gallons. Based on this information, what is the constant of proportionality?

25

15

375

10

Answers

Answer:

15

Step-by-step explanation:

[tex]\frac{25}{375} = \frac{1}{x}[/tex]

Cross multiply to get 25x = 375

Divide each side by 25 to get x = 15

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