Lesson 13

Polynomial Division (Part 2)

The practice problem answers are available at one of our IM Certified Partners

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.

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?

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:

$(x+8)$

Problem 4

Match the polynomial function with its constant term.

(From Algebra2, Unit 2, Lesson 6.)

Problem 5

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

(From Algebra2, 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?

polynomial function graphed. x intercepts = -4, 0, and 3. y intercept = 0. f of x increases as x increases. 
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.

(From Algebra2, 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.
(From Algebra2, Unit 2, Lesson 12.)