# Lesson 6

Different Forms

### Problem 1

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

- 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.

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

### Problem 3

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

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

### Problem 4

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

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

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

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

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

### Problem 5

Select **all** polynomial expressions that are equivalent to \(5x^3 +7x - 4x^2 + 5\).

$13x^{5}$

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

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

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

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

### Problem 6

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

Point $A$

Point $B$

Point $C$

Point $D$

Point $E$

Point $F$

Point $G$

### Problem 7

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