# Lesson 6

Different Forms

• Let’s use the different forms of polynomials to learn about them.

### Problem 1

$$f(x)=(x+3)(x-4)$$ and $$g(x)=\frac13(x+3)(x-4)$$. The graphs of each are shown here.

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

### Problem 2

For each polynomial function, rewrite the polynomial in standard form. Then state its degree and constant term.

1. $$f(x)=(x+1)(x+3)(x-4)$$
2. $$g(x)=3(x+1)(x+3)(x-4)$$

### Problem 3

Tyler incorrectly says that the constant term of $$(x + 4)(x - 4)$$ is zero.

1. What is the correct constant term?
2. What is Tyler’s mistake? Explain your reasoning.

### Problem 4

Which of these standard form equations is equivalent to $$(x+1)(x-2)(x+4)(3x+7)$$?

A:

$$x^4 + 10x^3 + 15x^2 - 50x - 56$$

B:

$$x^4 + 10x^3 + 15x^2 - 50x + 56$$

C:

$$3x^4 + 16x^3 + 3x^2 - 66x - 56$$

D:

$$3x^4 + 16x^3 + 3x^2 - 66x + 56$$

### Problem 5

Select all polynomial expressions that are equivalent to $$5x^3 +7x - 4x^2 + 5$$.

A:

$$13x^{5}$$

B:

$$5x^3 - 4x^2 + 7x + 5$$

C:

$$5x^3 + 4x \boldcdot 2 + 7x + 5$$

D:

$$5 + 4x - 7x^2 + 5x^3$$

E:

$$5 + 7x - 4x^2 + 5x^3$$

(From Unit 2, Lesson 2.)

### Problem 6

Select all the points which are relative minimums of this graph of a polynomial function.

A:

Point $$A$$

B:

Point $$B$$

C:

Point $$C$$

D:

Point $$D$$

E:

Point $$E$$

F:

Point $$F$$

G:

Point $$G$$

(From Unit 2, Lesson 3.)

### Problem 7

What are the $$x$$-intercepts of the graph of $$y=(3x+8)(5x-3)(x-1)$$?

(From Unit 2, Lesson 5.)