Question

How do you factor `3x^2-7x+4` by grouping?

Answer 1

`3x^2-7x+4 = (3x-4)(x-1)`

Explanation:

Note that `7 = 3+4`, so we can split the middle term as `-3x-4x` to be able to factor by grouping:

`3x^2-7x+4 = 3x^2-3x-4x+4`

`color(white)(3x^2-7x+4) = (3x^2-3x)-(4x-4)`

`color(white)(3x^2-7x+4) = 3x(x-1)-4(x-1)`

`color(white)(3x^2-7x+4) = (3x-4)(x-1)`