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

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Answer 1 · 2015-12-06T13:06:28

#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 #1+(-6)= -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) #