Posted by **lauren** on Wednesday, March 17, 2010 at 10:06pm.

Can you help with three problems 1)2x^2+7x+3 2)6x^2+5x-4 3)4x^2+12x+9 I have to factor this problems.Please help

- math -
**Reiny**, Wednesday, March 17, 2010 at 10:34pm
What methods have you been taught?

- math -
**Anonymous**, Wednesday, March 17, 2010 at 10:49pm
FACTORING

- math -
**Reiny**, Wednesday, March 17, 2010 at 11:05pm
What methods of factoring quadratic trinomials have you been taught ?

Does decomposition ring a bell?

- math -
**Anonymous**, Wednesday, March 17, 2010 at 11:09pm
no

- math -
**Reiny**, Wednesday, March 17, 2010 at 11:21pm
I will do the second one for you

6x^2+5x-4

multiply the first and last coefficients,

6 x -4 = -24

now look for 2 factors of -24 which have a sum of 5, the middle term coefficient.

I think -3 and 8 will do it.

so (-3)(8) = -24 and

(-3) + (8) = 5

so we will now "decompose" the middle term of 5x into -3x + 8x

then 6x^2+5x-4

= 6x^2 - 3x + 8x - 4

Now factor it in pairs,

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

Notice that (2x - 1) is a common factor

This must always happen!

If you have found the combination for the multiplication and addition correctly you WILL HAVE A COMMON FACTOR

so

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

There are other methods, but this one seems to be a common method taught these days. Although it might seem long, it is easy to understand and if factors exist, it will always work.

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