Question

Explain, in complete sentences, how you would factor 5x^3 – 35x^2 + 60x

Answer 1

Each coefficient is a multiple of 5x, so first I would factor out 5x. This would leave me with 5x * (x^2 - 7x + 12)

Now, because the first sign is negative and the second positive, I am looking for factors of the quadratic that look like (x - ?) and (x - ?).

Since 4 and 3 multiply to 12 and add to 7, I'm going to think these factors are (x - 4) and (x - 3).

This gives me, as my solution, 5x(x - 4)(x - 3)