How do you factor #10x^2+31x-14#?

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Answer 1 · 2015-05-06T12:59:53

We can Split the Middle Term of this expression to factorise it

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 10*-14 = -140#
AND
#N_1 +N_2 = b = 31#

After trying out a few numbers we get #N_1 = 35# and #N_2 =-4#

#35*-4 = -140#, and #35+(-4)= 31#

#10x^2+31x-14 = 10x^2 +35x - 4x - 14#

# = 5x(2x+7) - 2(2x+7)#

#2x+7# is a common factor to each of the terms

#=color(green)((2x+7)(5x-2)#