1. Introduction to Factoring
5.1
Factoring Monomials
Factoring When Terms Have a Common Factor
Factoring by Grouping
Checking by Evaluating

2. Factoring
To factor a polynomial is to find an equivalent expression that is a product. An equivalent expression of this type is called a factorization of the polynomial.

3. Find three factorizations of 24x3
Find three factorizations of 24x3. Solution a) 24x3 = b) 24x3 = c) 24x3 =

4. Factoring When Terms Have a Common Factor
To factor a polynomial with two or more terms of the form ab + ac, we use the distributive law with the sides of the equation switched: ab + ac = a(b + c). Multiply Factor 4x(x2 + 3x  4) 4x3 + 12x2  16x

5. Factor: 9a  21. Solution

6. Sage and Scribe
Factor: 9a3b4 + 18a2b3
Solution
Factor: 28x6 + 32x3.
Solution

7. Factor: 12x5  21x4 + 24x3
Solution

8. Factor: 4xy + 8xw  12x Solution

9. Tips for Factoring
1. Factor out the largest common factor, if one exists.
2. The common factor multiplies a polynomial with the same number of terms as the original polynomial.
3. Factoring can always be checked by multiplying. Multiplication should yield the original polynomial.

10. Factor x2(x + 2) + 3(x + 2). Solution

11. If a polynomial can be split into groups of terms and the groups share a common factor, then the original polynomial can be factored. This method, known as factoring by grouping, can be tried on any polynomial with four or more terms.

12. Sage and Scribe Factor by grouping. a) 3x3 + 9x2 + x + 3
b) 9x4 + 6x  27x3  18