Factoring Trinomials
|
Perfect Square Trinomial |
| a2 + 2ab + b2 = (a + b)(a
+ b) |
a2 - 2ab + b2 = (a - b)(a
- b) |
|
Difference of Two Squares
a2 - b2 = (a + b)(a - b) |
| Sum of Two Cubes
a3 + b3 = (a + b)(a2 - ab + b2) |
Difference of Two Cubes
a3 - b3 = (a - b)(a2 + ab + b2) |
A General Strategy for Factoring
You have factored polynomials using a variety of methods. Some factoring
problems require more than one method. Here is a systematic procedure
for factoring a polynomial.
Procedure —
General Strategy for Factoring a Polynomial
Step 1 Factor out the GCF of the terms of the polynomial.
Step 2 Count the number of terms and look for factoring patterns.
Two Terms: Look for the difference of two squares, the sum of
two cubes, or the difference of two cubes.
Three Terms:
• Look for a perfect square trinomial.
• If the trinomial has the form x2 + bx + c, try to find two integers whose product is c
and whose sum is b.
• If the trinomial has the form ax2 + bx + c, try to find two integers whose product is ac
and whose sum is b.
Four Terms: Try factoring by grouping.
Step 3 Factor completely.
To check the factorization, multiply the factors.
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