How do you factor #3x^2 + 13x - 10 # by grouping?

1 Answer
Shwetank Mauria
Aug 31, 2016

#3x^2+13x-10=(3x-2)(x+5)#

Explanation:

Let the quadratic polynomial to be factorized be #ax^2+bx+c#. To factorize using grouping method, one needs to split middle term #b# in two parts, so that their sum is #b# and product is #a×c#.

In #3x^2+13x-10#, we should split #13# in two parts so that their product is #3×(-10)=-30#. Sich numbers are #15# and #-2# and hence

#3x^2+13x-10#

= #3x^2+15x-2x-10#

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

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

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