# 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.

- 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 \(y=(3x+8)(5x-3)(x-1)\)?