I have been looking into the different methods used to factor polynomials. I came across this example 12x^{2} – 7x – 10, apart from finding its zeroes is there another method that works for this case ?
I have been looking into the different methods used to factor polynomials. I came across this example 12x^{2} – 7x – 10, apart from finding its zeroes is there another method that works for this case ?
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:
$\displaystyle 12x^2–7x–10=(4x-5)(3x+2)$