I have been looking into the different methods used to factor polynomials. I came across this example 12xapart from finding its zeroes is there another method that works for this case ?^{2}– 7x – 10,

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- Nov 15th 2012, 10:06 PMtheintervurtPolynomial factorization methods
I have been looking into the different methods used to factor polynomials. I came across this example 12

*x*apart from finding its zeroes is there another method that works for this case ?^{2}– 7*x – 10,* - Nov 15th 2012, 10:17 PMMarkFLRe: Polynomial factorization methods
You can look for two factors of the product of the first and last coefficients $\displaystyle 12(-10)=-120$ whose sum is the middle coefficient. We find:

$\displaystyle 8(-15)=-120$ and $\displaystyle 8+(-15)=-7$

Next, we observe that $\displaystyle 8=2(4)$ and $\displaystyle -15=-5(3)$ and we need $\displaystyle 4(3)=12$ and $\displaystyle 2(-5)=-10$ hence, we may state:

$\displaystyle 12x^2–7x–10=(4x-5)(3x+2)$