Question

How do you factor the expression `x^2 +7x-8`?

Answer 1

`x^2+7x-8 = (x-1)(x+8)`

Explanation:

Given `x^2+7x-8`

Note that the sum of the coefficients is `0`. That is `1+7-8 = 0`.

So `x=1` is a zero and `(x-1)` a factor:

`x^2+7x-8 = (x-1)(x+8)`

The linear factor `(x+8)` can be constructed by looking at the coefficients of `x^2` and the constant term `-8` that we want in the product:

• Since the coefficient of `x^2` is `1` in the product, we require a coefficient `1` for `x`.

• Since the constant term is `-8` in the product, we require a constant `+8` in the factor which will become `-8` when multiplied by `-1`.