How do you factor #10x^2+3x-4#?

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Answer 1 · 2015-08-10T15:29:12

#color(blue)((2x-1)( 5x +4)# is the factorised form of the expression.

#10x^2+3x−4#

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*-4 = -40#
and,
#N_1 +N_2 = b = 3#

After trying out a few numbers we get #N_1 = 8# and #N_2 =-5#
#8*-5 = -40#, and #8+(-5)=3#

#10x^2+color(blue)(3x)−4 = 10x^2+color(blue)(8x - 5x)−4#

#=2x( 5x +4)−1(5x+4)#

#color(blue)((2x-1)( 5x +4)# is the factorised form of the expression.