How do you factor #8x^2+2x-1#?

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Answer 1 · 2016-05-14T06:57:15

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

#8x^2 + 2x - 1 #

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 = 8*(-1) = -8#

AND

#N_1 +N_2 = b = 2#

After trying out a few numbers we get #N_1 = 4# and #N_2 =-2#
#4*(-2) = -8#, and #4+(-2)= 2#

#8x^2 + 2x - 1 =8x^2 + color(blue)(4x - 2x) - 1#

# = 4x(2x + 1 ) - 1( 2x + 1 )#

#(2x + 1 )# is a common factor to each of the terms

# = color(green)((4x - 1 ) (2x + 1 ) #