Remember when we learned how to solve linear equations? Well, guess what, we were solving a polynomial!
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
While a linear equation is a first-degree polynomial, where we don’t need to factor before we solve, some of these same skills will undoubtedly help us to solve polynomial equations by factoring.
So we begin by focusing on the number zero!
Why?
When we have a product of two or more factors, the only way for the product to equal zero is for one or more of the factors to also equal zero.
In other words, for all real numbers a and b,
The Zero-Product Property
We call this property, the Zero Product Theorem, as Wyzant so accurately states, we will use this important rule of zero when we are solving by factoring.
So, what are the steps for solving an equation by factoring?
- Write the polynomial in standard form all on one side of the equation set equal to zero.
- Factor the polynomial and write as a product of factors.
- Set each factor equal to zero and solve for the variable using our SCAM technique.
In this lesson, we’re going to expand our skills to solve polynomials of all different degrees such as solving quadratic equations (degree 2 polynomial), cubic equations (degree 3 polynomials), and more.
Solve By Factoring (How-To) – Video
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