How do you factor #8x^2+6x+1#?

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Answer 1 · 2015-09-23T12:49:42

#=color(blue)((2x+1) (4x +1)#

#8x^2 + 6x +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 = 6#

After trying out a few numbers we get #N_1 = 2# and #N_2 =4#

#2 *4 = 8# and #2 + 4= 6#

#8x^2 + color(blue)(6x) +1 =8x^2 + color(blue)(2x +4x) +1 #

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

#=color(blue)((2x+1) (4x +1)#