Question

Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this?

Show your answer using both words and mathematical notation.

Answer 1

The first one: x^2 + bx + c factors into two binomial fo the form (x + p)(x + q)
where pq = c and p + q = b.
In words, you need to find two numbers that multiply to c and add to b.

Answer 2

The second one, ax^ + bx + c, factors into (px + q)(rx + s) where pq = a, qs = c, and ps + qr = b.
In words, you need to find 4 numbers. The first two (call them p,r) must be factors of a, and the other two (call them q and s) must be factors of c. p, q, r, s must be chosen so that they satisfy this ps + qr = b.

Answer 3

sorry I posted this one wrong its in the wrong fomat the correct one is posted