Question

How do you use the factor theorem to determine whether x-5 is a factor of `3x^2 + 7x + 40`?

Answer 1

Substitute `x=5` and see if the result is `0`.

Explanation:

If `f(x) = 3x^2+7x+40` then `(x-5)` is a factor if and only if `f(5) = 0`

We find:

`f(5) = 3*5^2+7*5+40 = 75+35+40 = 150 != 0`

So `(x-5)` is not a factor.

In fact we can tell that `3x^2+7x+40` has no factors with Real coefficients, since its discriminant is negative:

`Delta = b^2-4ac = 7^2-(4*3*40) = 49-480 = -431`