# math

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What methods have you been taught?

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FACTORING

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What methods of factoring quadratic trinomials have you been taught ?

Does decomposition ring a bell?

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no

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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.