Factoring Polynomials by Grouping
Example
Factor: 6wx^{2} + 18wxy + 3wx + 9wy
Solution
Step 1 Factor each term.
6wx^{2} + 18wxy + 3wx + 9wy
Each term of the polynomial has 3w as a factor.
= 2 Â· 3
Â· w Â·
x Â· x + 2 Â·
3 Â· 3 Â·
w Â· x Â· y
+ 3 Â· w
Â· x + 3
Â· 3 Â· w
Â· y
So before we group, we factor out 3w.
= 3w[2 Â· x
Â· x + 2 Â· 3
Â· x Â· y
+ x + 3 Â· y]
Step 2 Group terms with common factors.
Within the brackets, 2 and x are factors of the first and second terms.
Therefore, group those terms together.
= 3w[(2 Â· x
Â· x + 2
Â· 3 Â· x
Â· y) + (1
Â· x + 1
Â· 3 Â· y)]
