How to Factor PolynomialsLet's face it: if you want to pass algebra, you will have to know how to factor polynomials. First Question: Does your polynomial have a GCF?
Second Question: How manyterms does your polynomial have?
Need to know how to solve quadratic equations (equations with x2)? Learn to use thequadratic formula.
Remember, make sure to always factor out a GCF first. Sometimes that's the only part of the binomial that can be factored. Once you have checked for the GCF, then you can move forward... If you are taking a basic algebra class, you probably only need to know one type of factoring when you have two terms: its called the difference of two squares. You need to know how to factor the difference of two squares if you want to know how to factor polynomials.
More examples of the difference of two squares. Notice, every number is a perfect square - which means there is some number times itself that gives you that number.
Now, onto the factoring...
x2 - 16 factors to (x + 4)(x - 4) 4x2 - 49 factors to (2x + 7)(2x - 7) Notice how each factor breaks down as ...
Difference of 2 Cubes: (x3− y3) = (x − y)(x2 + xy + y2) Sum of 2 Cubes: (x3 + y3) = (x + y)(x2− xy + y2) Note: You can factor the sum of 2 cubes, but you cannot factor the sum of 2 squares!
Method 1: Guess/Check. Best used when the a value is 1(more info) After you have "guessed" at the numbers 5 and 3, check them using FOIL. Method 2: The British Method: Best used when the a value is > 1. Most beginning students prefer this method when trying to learn how to factor polynomials.
Think you knowhow to factor polynomials? You might want to also look at the reverse process of factoring: expanding. This process is often called FOILing. Explore other topics on factoring or return to the GradeA homepage.
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