Question

If one of the factors of `3x^2 + 8x - 35` is `3x - 7`, how do you find the other factor?

Answer 1

The solution is `(x+5)`..

We want to find `a` and `b`, so that `(3x-7)(ax+b) = 3x^2+8x-35`.

Let's just expand this some more:
`(3x-7)(ax+b) = 3x^2*a+3x*b-7x*a-7b`.

We want `3x^2*a` to be equal to `3x^2`, so `a` should be equal to one. We want `-7b` to be equal to `-35`, so `b` should be equal to `5`.
Now we need to check this solution:
`(3x-7)(ax+b) = (3x-7)(x+5) = 3x^2+8x-35`. This is correct, so the factor we should multiply by is `(x+5)`.