# Lesson 10

Multiplicity

### Problem 1

Draw a rough sketch of the graph of $$g(x)=(x-3)(x+1)(7x-2)$$.

### Solution

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### Problem 2

Draw a rough sketch of the graph of $$f(x)=(x+1)^2(x-4)$$.

### Solution

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### Problem 3

Technology required. Predict the end behavior of each polynomial function, then check your prediction using technology.

1. $$A(x) = (x + 3)(x - 4)(3x - 7)(4x - 3)$$
2. $$B(x) = (3 - x)^2(6 - x)$$
3. $$C(x) = \text-(4 - 3x)(x^4)$$
4. $$D(x) = (6 - x)^6$$

### Solution

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### Problem 4

Which term can be added to the polynomial expression $$5x^{7}-6x^{6}+4x^4-4x^2$$ to make it into a 10th degree polynomial?​​

A:

10

B:

$$5x^3$$

C:

$$5x^7$$

D:

$$x^{10}$$

### Solution

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(From Unit 2, Lesson 3.)

### Problem 5

$$f(x)=(x+1)(x-6)$$ and $$g(x)=2(x+1)(x-6)$$. The graphs of each are shown.

1. Which graph represents which polynomial function? Explain how you know.

### Solution

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(From Unit 2, Lesson 6.)

### Problem 6

State the degree and end behavior of $$f(x)=8x^3+2x^4-5x^2+9$$. Explain or show your reasoning.

### Solution

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(From Unit 2, Lesson 8.)

### Problem 7

The graph of a polynomial function $$f$$ is shown. Select all the true statements about the polynomial.

A:

The degree of the polynomial is even.

B:

The degree of the polynomial is odd.

C:

The leading coefficient is positive.

D:

The leading coefficient is negative.

E:

The constant term of the polynomial is positive.

F:

The constant term of the polynomial is negative.

### Solution

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(From Unit 2, Lesson 9.)
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