Lesson 7

Using Factors and Zeros

  • Let’s write some polynomials.

Problem 1

Diego wrote \(f(x)=(x+2)(x-4)\) as an example of a function whose graph has \(x\)-intercepts at \(x=\text-4,2\). What was his mistake?

Problem 2

Write a possible equation for a polynomial whose graph has horizontal intercepts at \(x=2,\text-\frac12,\text-3\).

Problem 3

Which polynomial function’s graph is shown here?

Coordinate plane, x, negative 5 to 3 by 1, y axis negative 25 to 10 by 5. Curve begins in the third quadrant, through negative 4 comma 0, negative 1 comma 0, negative y-intercept, through 3 comma
A:

\(f(x)=(x+1)(x+3)(x+4)\)

B:

\(f(x)=(x+1)(x-3)(x+4)\)

C:

\(f(x)=(x-1)(x+3)(x-4)\)

D:

\(f(x)=(x-1)(x-3)(x-4)\)

Problem 4

Which expression is equivalent to \((3x + 2)(3x - 5)\)?

A:

\(6x - 3\)

B:

\(9x^2 - 10\)

C:

\(9x^2 -3x - 10\)

D:

\(9x^2-9x - 10\)

(From Unit 2, Lesson 4.)

Problem 5

What is the value of \(6(x-2)(x-3)+4(x-2)(x-5)\) when \(x=\text-3\)?

(From Unit 2, Lesson 5.)

Problem 6

Match each polynomial function with its leading coefficient.

A:

\(P(x)=(x+2)(2x-3)(4x+7)\)

B:

\(P(x)=\frac12(x-2)(2x-3)(4x+7)\)

C:

\(P(x)=5(x-2)(2x-3)(4x+7)\)

D:

\(P(x)=\text-(x-2)(2x-3)(4x+7)\)

E:

\(P(x)=\frac{1}{4}(x+2)(2x-3)(4x+7)\)

1:

40

2:

8

3:

4

4:

2

5:

-8

(From Unit 2, Lesson 6.)