Question

6. a. Find the factors of: 9 * (p + q) ^ 2 + (p + q) - 8​

Answer 1

(9p + 9q - 8)(p + q + 1)

Explanation:

Treat p + q as x. Then this is a quadratic trinomial in x.

9(p + q)² + (p + q) - 8 =

= [9(p + q) - 8][(p + q) + 1]

= (9p + 9q - 8)(p + q + 1)

It may be easier for you to see it if you actually make a substitution:

Let x = p + q.

9(p + q)² + (p + q) - 8 =

Let x = p + q.

= 9x² + x - 8

Now factor the quadratic trinomial.

= (9x - 8)(x + 1)

Now substitute back p + q for x.

= [9(p + q) - 8][p + q + 1)

= (9p + 9q - 8)(p + q + 1)