How do you factor #2x^2+5x-3 #?

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Answer 1 · 2015-08-11T16:50:22

#color(blue)((2x-1)(x+3)# is the factorised form of the expression.

#2x^2+5x−3#
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 = 2*(-3) = -6#
and
#N_1 +N_2 = b = 5#

After trying out a few numbers we get #N_1 = 6# and #N_2 =-1#

#6*(-1) = -6#, and #6+(-1)=5#

#2x^2+color(blue)(5x)−3 = 2x^2+color(blue)(6x -1x)−3 #

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

#color(blue)((2x-1)(x+3)# is the factorised form of the expression.