How do you factor the trinomial $x² - 7x + 12$ ?

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Answer 1 · 2015-12-23T17:12:23

$color(blue)((x -4) (x-3)$ is the factorised form of the expression.

$x^2-7x+12$

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:

$N_1*N_2 = a*c = 1*12 =12$

AND

$N_1 +N_2 = b = -7$

After trying out a few numbers we get $N_1 = -3$ and $N_2 =-4$
$-3*-4 = 12$ , and $(-3)+(-4)= -7$

$x^2color(blue)(-7x)+12 = x^2color(blue)(-3x-4x)+12$

$=x (x-3) -4(x-3)$

$color(blue)((x -4) (x-3)$ is the factorised form of the expression.

How do you factor the trinomial x² - 7x + 12x² - 7x + 12?