Question

Why is factoring out a gcf helpful

Answer 1

Factoring out a gcf in factoring helps tons when it leaves the first coefficient equal to 1. For example, take
`4x^(2) +16x+16` Looks complicated to factor, right? But we see that taking out 4 is possible, which will leave us with an easier equation to factor:
`4(x^(2) +4x+4)= 4(x+2)^2`

Answer 2

The short answer: it simplifies your problem. The equation

`169x+91=0`

seems intimidating at first, but we can use that fact that 169 and 91 have the greatest common factor 13 (169 = 13 x 13 and 91 = 13 x 7) to rewrite this as

`image`

and from there, it's much less of a headache to work out.