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- welshfella

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

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- welshfella

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

- katieb

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- welshfella

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)

- welshfella

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.

- anonymous

good job :)

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- ali2x2

Huh, nice work

- mathmate

:)

- Nnesha

This is called the *headphone* method :P

- Nnesha

thats what my teacher told us . |dw:1438711610806:dw|
looks like a headphone ? lol

- welshfella

yes that's a good way to remember it !

- welshfella

|dw:1438711718282:dw|

- Nnesha

yeah that^^
nvm :) nice work!

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