What are the factors of q3-q2 plus 2q-2?

Answer 1

Factoring the left and right parts separately gives:

q3 - q2 + 2q - 2

= q(q2 - 1) + 2(q - 1)

= q(q + 1)(q - 1) + 2(q - 1)

Now we have a common factor (q - 1) that we can take out. I'll combine the remaining terms again:

(q - 1)[q(q + 1) + 2(q - 1)]

= (q - 1)[q2 + q + 2q - 2]

= (q - 1)(q2 + 3q - 2)

The right part has no obvious factorization; but you can use the quadratic formula to get the factors, which will probably include square roots.