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

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

How do you factor 8x^2+2x-18x^2+2x-1?