Lesson 2
1. Lesson 2
1.7. Explore 3
Module 4: Quadratic Equations and Inequalities
Equations of the Quadratic Type
Can you see the quadratic form in this polynomial: 4(x + 2)2 − 9(x − 1)2?
What if you let t = (x + 2) and r = (x − 1)? Now can you see the quadratic form 4t2 − 9r2?
As you saw in part a of “Example 2” in the textbook, you can use a method of replacing a binomial with a single variable to temporarily “declutter” the quadratic. You can then factor the quadratic using a method your are familiar with. When the math is done, the expressions t = (x + 2) and r = (x − 1) are placed back into your final expression.
It is important to include the brackets around the binomials when placing the binomials back into your expression because, in some cases, a sign may change.
In Try This 2 you may have used a factoring strategy similar to the one used in “Example 2,” part b. This strategy applies the difference-of-squares factoring pattern P2 − Q2 = (P − Q)(P + Q) to any polynomial in quadratic form.
It does not matter which method you choose; the final factored form will be the same.
Self-Check 1
