Factoring

Intro

Factoring is used in many areas of math, specifically pre-calculus. It’s used almost throughout the entire course. Many students have issues with factoring correctly which is why I’m going to show a sample problem solving a quadratic equation with factoring.

Sample Problem

Solve by factoring:
2x^2-5x+2=0

Solution

We start by creating two sets of parentheses:
( )( )
We then factor the trinomial on the left. We try to find two monomials that have the product of 2x^2. We find that 2x and x works. 2x goes into first set of parentheses and x goes into the second set of parentheses:
(2x )(x )
Then we try to find the other two constants that have a product of positive 2 and inner product/outer product sum of negative 5x. This is achieved by -1 and -2. After we plug those numbers in, we set the entire equation set to 0.
(2x-1)(x-2)=0
We solve each set of parentheses individually in order to get our two values for x:
2x-1=0
2x=1
x=1/2 is one solution.
x-2=0
x=2 is the second solution.

You have now solved the quadratic equation by factoring and found the two values of x.



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