math
posted by lauren .
Can you help with three problems 1)2x^2+7x+3 2)6x^2+5x4 3)4x^2+12x+9 I have to factor this problems.Please help

math 
Reiny
What methods have you been taught?

math 
Anonymous
FACTORING

math 
Reiny
What methods of factoring quadratic trinomials have you been taught ?
Does decomposition ring a bell? 
math 
Anonymous
no

math 
Reiny
I will do the second one for you
6x^2+5x4
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+5x4
= 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
= (2x1)(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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