Question

Factor x^2 - 6x + 8

Explain the factoring by grouping method

Answer 1

The correct answer is (x-2)(x-4).

Answer 2

We know that
`8=2\cdot4`, and that
`-(2+4)=-6`. Then if we write

`x^2-6x+8=x^2-4x-2x+8=(x^2-4x)+(-2x+8)`

then pull out common factors from the grouped terms to get

`x(x-4)-2(x-4)`

we can apply the distributive property to end up with the factorization

`(x-2)(x-4)`