# Lesson 13

Polynomial Division (Part 2)

### Problem 1

The polynomial function $$B(x)=x^3-21x+20$$ has a known factor of $$(x-4)$$. Rewrite $$B(x)$$ as a product of linear factors.

### Solution

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### Problem 2

Let the function $$P$$ be defined by $$P(x) = x^3 + 7x^2 - 26x - 72$$ where $$(x+9)$$ is a factor. To rewrite the function as the product of two factors, long division was used but an error was made:

$$\displaystyle \require{enclose} \begin{array}{r} x^2+16x+118\phantom{000} \\ x+9 \enclose{longdiv}{x^3+7x^2-26x-72} \phantom{000}\\ \underline{-x^3+9x^2} \phantom{-26x-720000} \\ 16x^2-26x \phantom{-720000}\\ \underline{-16x^2+144x} \phantom{-20000} \\ 118x-72 \phantom{00} \\ \underline{-118x+1062} \\ 990 \end{array}$$

How can we tell by looking at the remainder that an error was made somewhere?

### Solution

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### Problem 3

For the polynomial function $$A(x)=x^4-2x^3-21x^2+22x+40$$ we know $$(x-5)$$ is a factor. Select all the other linear factors of $$A(x)$$.

A:

$$(x+1)$$

B:

$$(x-1)$$

C:

$$(x+2)$$

D:

$$(x-2)$$

E:

$$(x+4)$$

F:

$$(x-4)$$

G:

$$(x+8)$$

### Solution

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### Problem 4

Match the polynomial function with its constant term.

### Solution

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(From Unit 2, Lesson 6.)

### Problem 5

What are the solutions to the equation $$(x-2)(x-4)=8$$?

### Solution

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(From Unit 2, Lesson 11.)

### Problem 6

The graph of a polynomial function $$f$$ is shown. Which statement is true about the end behavior of the polynomial function?

A:

As $$x$$ gets larger and larger in the either the positive or the negative direction, $$f(x)$$ gets larger and larger in the positive direction.

B:

As $$x$$ gets larger and larger in the positive direction, $$f(x)$$ gets larger and larger in the positive direction. As $$x$$ gets larger and larger in the negative direction, $$f(x)$$ gets larger and larger in the negative direction.

C:

As $$x$$ gets larger and larger in the positive direction, $$f(x)$$ gets larger and larger in the negative direction. As $$x$$ gets larger and larger in the negative direction, $$f(x)$$ gets larger and larger in the positive direction.

D:

As $$x$$ gets larger and larger in the either the positive or negative direction, $$f(x)$$ gets larger and larger in the negative direction.

### Solution

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(From Unit 2, Lesson 8.)

### Problem 7

The polynomial function $$p(x)=x^3+3x^2-6x-8$$ has a known factor of $$(x+4)$$.

1. Rewrite $$p(x)$$ as the product of linear factors.
2. Draw a rough sketch of the graph of the function.

### Solution

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(From Unit 2, Lesson 12.)