How do you factor $x^2 - 10x + 24$ ?

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Answer 1 · 2015-05-03T12:11:35

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:

$N_1*N_2 = a*c = 1*24 = 24$
AND
$N_1 +N_2 = b = -10$

After trying out a few numbers we get $N_1 = -6$ and $N_2 =-4$

$-6*-4 = 24$ , and $(-6)+(-4)= -10$

$x^2 - 10x + 24 = x^2 - 6x - 4x +24$

$= x(x-6) - 4(x - 6)$

$(x - 6)$ is a common factor to each of the terms

$= color(green)((x-6)(x-4)$

How do you factor x^2 - 10x + 24x^2 - 10x + 24?