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

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

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Answer 1 · 2015-09-16T16:17:32

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

Explanation:

$x^{2} - x - 42$ $x^2−x−42$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot - 42 = - 42$ $N_1*N_2 = a*c = 1*-42 = -42$
AND
$N_{1} + N_{2} = b = - 1$ $N_1 +N_2 = b = -1$

After trying out a few numbers we get $N_{1} = - 7$ $N_1 = -7$ and $N_{2} = 6$ $N_2 =6$
$- 7 \cdot 6 = - 42$ $-7*6 = -42$ and $- 7 + 6 = - 1$ $-7+6=-1$

$x^{2} - x - 42 = x^{2} - 7 x + 6 x - 42$ $x^2−x−42=x^2−7x+6x−42$

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

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

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

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