# Lesson 5

Connecting Factors and Zeros

- Let’s investigate polynomials written in factored form.

### 5.1: Notice and Wonder: Factored Form

What do you notice? What do you wonder?

### 5.2: What Values of $x$ Make These Equations True?

Find all values of \(x\) that make the equation true.

- \((x+4)(x+2)(x-1)=0\)
- \((x+4)(x+2)(x-1)(x-3)=0\)
- \((x+4)^2 (x+2)^2=0\)
- \(\text-2(x-4)(x-2)(x+1)(x+3)=0\)
- \((2x+8)(7x-3)(x-10)=0\)
- \(x^2+3x-4=0\)
- \(x(3-x)(x-1)(x+0.75)=0\)
- \((x^2-4)(x+9)=0\)

- Write an equation that is true when \(x\) is equal to -5, 4, or 0 and for no other values of \(x\).
- Write an equation that is true when \(x\) is equal to -5, 4, or 0 and for no other values of \(x\), and where one side of the equation is a 4th degree polynomial.

### 5.3: Factors, Intercepts, and Graphs

Your teacher will give you a set of cards. Match each equation to either a graph or a description.

Take turns with your partner to match an equation with a graph or a description of a graph.

- For each match that you find, explain to your partner how you know it’s a match.
- For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.

### Summary

When a polynomial is written as a product of linear factors, we can identify several facts about it.

For example, the factored form of the polynomial shown in the graph is \(P(x)=0.5(x-3)(x-2)(x+1)\).