Lesson 7

Using Factors and Zeros

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?

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:

$$9x^2-9x - 10$$

Solution

(From Unit 2, Lesson 4.)

Problem 5

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