Factoring Trinomials
Perfect Square Trinomial 
a^{2} + 2ab + b^{2} = (a + b)(a
+ b) 
a^{2}  2ab + b^{2} = (a  b)(a
 b) 
Difference of Two Squares
a^{2}  b^{2} = (a + b)(a  b) 
Sum of Two Cubes
a^{3} + b^{3} = (a + b)(a^{2}  ab + b^{2}) 
Difference of Two Cubes
a^{3}  b^{3} = (a  b)(a^{2} + ab + b^{2}) 
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 â€”
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:
â€¢ Look for a perfect square trinomial.
â€¢ If the trinomial has the form x^{2} + bx + c, try to find two integers whose product is c
and whose sum is b.
â€¢ If the trinomial has the form ax^{2} + 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.
