Which factors p and q add to equal the coefficient of the x term (-15) in the trinomial

Question

Which factors for p and q add to equal the coefficient of the x-term (-15) in the trinomial

Answer 1

When factoring a trinomial like x2+bx+cx^2 + bx + cx2+bx+c, we look for two numbers p and q that add to the x-term coefficient and multiply to the constant term.

In this question, the x-term coefficient is −15, so we need two numbers that add to −15.

Examples of possible pairs are:

1. −1 and −14
2. −2 and −13
3. −3 and −12
4. −5 and −10
5. −6 and −9
6. −7 and −8

Each pair works because their sum is −15.

To determine the correct pair, we would also check which pair multiplies to the constant term in the trinomial.