Close this window

Factoring by Grouping

You can sometimes factor a difficult-looking polynomial by making creative use of the distributive property.

You can get a clue from the coefficients: we have a 2 and a –6, and we also have a 3 and a –9. There is a proportional relationship here which can be exploited!

Factor 2x out of the first two terms:

2xy – 6xz + 3y – 9z = 2x(y – 3z) + 3y – 9z

Then factor 3 out of the second two terms.

= 2x(y – 3z) + 3(y – 3z)

Since the same quantity y – 3z appears twice, we can use the distributive property to write this more simply:

= (2x + 3)(y – 3z)

Group the terms as follows:

x² + xy + 3x + 3y = (x² + 3x) + (xy + 3y)

Both groups have x + 3 as a factor.

= x(x + 3) + y(x + 3)

= (x + y)(x + 3)