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
What methods have you been taught?
FACTORING
What methods of factoring quadratic trinomials have you been taught ?
Does decomposition ring a bell?
no
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.