# 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?

### Solution

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### Problem 2

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

### Solution

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### Problem 3

Which polynomial function’s graph is shown here?

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

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

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

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

### Solution

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### Problem 4

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

\(6x - 3\)

\(9x^2 - 10\)

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

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

### Solution

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(From Unit 2, Lesson 4.)### Problem 5

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

### Solution

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(From Unit 2, Lesson 5.)### Problem 6

Match each polynomial function with its leading coefficient.

### Solution

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(From Unit 2, Lesson 6.)