Asked by lauren

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
Answered by Reiny
What methods have you been taught?

Answered by Anonymous
FACTORING
Answered by Reiny
What methods of factoring quadratic trinomials have you been taught ?

Does decomposition ring a bell?
Answered by Anonymous
no
Answered by Reiny
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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