How do you factor the expressions $x^2+3x-4$ ?

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Answer 1 · 2016-03-03T18:06:50

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

$x^2 +3x -4$

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:

$N_1*N_2 = a*c = 1*-4 = -4$

AND

$N_1 +N_2 = b = 3$

After trying out a few numbers we get $N_1 = -1$ and $N_2 =4$
$-1*4 = -4$ , and $4+(-1)= 3$

$x^2 +3x -4 = x^2 +4x -1x-4$

$=x(x+4) - 1(x+4)$

$(x+4)$ is a common factor to each of the terms
$=(x-1) (x+4)$

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

How do you factor the expressions x^2+3x-4x^2+3x-4?