How do you factor the trinomial #4x^2-8x-5#?

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Answer 1 · 2016-03-15T15:24:57

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

#4x^2 -8x-5#

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 = 4*(-5) = -20#

AND

#N_1 +N_2 = b = -8#

After trying out a few numbers we get #N_1 = -10# and #N_2 =2#

#2*(-10) = -20#, and #2+(-10)= -8#

#4x^2 -8x-5 =4x^2 -10x+2x-5#

# = 2x(2x -5) +1 (2x -5)#

#(2x -5)# is a common factor to each of the terms.

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