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.
- \((x+4)^2 (x+2)^2=0\)
- 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.
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 \(P(x)=0.5(x-3)(x-2)(x+1)\).