How do you write $x^2-x-42$ in factored form?

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Answer 1 · 2015-09-16T16:17:32

$color(blue)((x+6)(x-7)$ is the factorised form of the expression.

$x^2−x−42$

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:

$N_1*N_2 = a*c = 1*-42 = -42$
AND
$N_1 +N_2 = b = -1$

After trying out a few numbers we get $N_1 = -7$ and $N_2 =6$
$-7*6 = -42$ and $-7+6=-1$

$x^2−x−42=x^2−7x+6x−42$

$=x(x-7)+ 6(x-7)$

$=color(blue)((x+6)(x-7)$

How do you write x^2-x-42x^2-x-42 in factored form?