Question

Short tutorial on the 'ac' method of factoring trinomials.

Answer 1

We have the standard form f(x) = ax^2 + bx + c . This is called the ac method because we start by multiplying the coefficient a by c.

An example will illustrate the method:-
Factor
4x^2 + 4x - 3

ac = 4*-3 = -12

Now factor -12:-

prime factors of -12 are -2*2*3

The middle term + 4x comes from adding 2 terms in x.
We are aiming to get the middle term + 4x - so, from the factors,
2*3x - 2x looks a good bet
So we write

4x^2 + 6x - 2x - 3

now we try to factor by grouping

in this case its easier to see how to do this if we reverse the order of the 2 middle terms

4x^2 - 2x + 6x - 3
= 2x(2x - 1) + 3(2x - 1)

2x - 1 is common to both parts so we have

(2x + 3)(2x - 1)

Answer 2

During my short teaching career I found quite a few pupils had problems with factoring these and this method is the one which most of them took to.

Answer 3

good job :)

Answer 4

Huh, nice work

Answer 5

:)

Answer 6

This is called the *headphone* method :P

Answer 7

thats what my teacher told us .
looks like a headphone ? lol