How do you factor #15x^2 - x-2#?

1 Answer
Shwetank Mauria
Jun 26, 2016

#15x^2-x-2=(3x+1)(5x-2)#

Explanation:

To factorize a quadratic polynomial #ax^2+bx+c#, if the discriminant #b^2-4ac# is a square f a rational number, then one can factorize it by splitting #b# in two parts whose product is #ac#.

Here discriminant is #(-1)^2-4*15*(-2)=1+120=121=11^2#, hence, one should split #15*(-2)=-30# in two parts so that their sum is #-1#. It is obvious these are #-6# and #5#.

Hence, #15x^2-x-2#

= #15x^2-6x+5x-2#

= #3x(5x-2)+1(5x-2)#

= #(3x+1)(5x-2)#

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