How do you factor $5x^2 + 8x - 4$ ?

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Answer 1 · 2016-04-07T09:27:49

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

$5x^2 + 8x - 4$

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:

$N_1*N_2 = a*c = 5 * ( - 4) = -20$

AND

$N_1 +N_2 = b = 8$

After trying out a few numbers we get $N_1 = 10$ and $N_2 =-2$
$10* (- 2) = -20$ , and $10+(-2)= 8$

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

$= 5x( x + 2 ) - 2 ( x + 2 )$

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

$= (5x - 2 ) ( x + 2 )$

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

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