Factoring Polynomials by Grouping

Example

Factor: 6wx² + 18wxy + 3wx + 9wy

Solution

Step 1 Factor each term.

6wx² + 18wxy + 3wx + 9wy

Each term of the polynomial has 3w as a factor.

= 2 · 3 · w · x · x + 2 · 3 · 3 · w · x · y + 3 · w · x + 3 · 3 · w · y

So before we group, we factor out 3w.

= 3w[2 · x · x + 2 · 3 · x · y + x + 3 · 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 · x · x + 2 · 3 · x · y) + (1 · x + 1 · 3 · y)]