How do you factor the expression $x^{2} - x - 42$ $x^2-x-42$ ?

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How do you factor the expression $x^{2} - x - 42$ $x^2-x-42$ ?

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Answer 1 · 2018-03-22T10:51:50

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

Explanation:

$x^{2} - x - 42$ $x^2-x-42$

$\Rightarrow x^{2} - 7 x + 6 x - 42$ $=> x^2-7x+6x-42$

$\Rightarrow x (x - 7) + 6 (x - 7)$ $=> x(x-7)+6(x-7)$

$\Rightarrow (x + 6) (x - 7)$ $=> (x+6)(x-7)$

Answer 2 · 2018-03-22T10:54:42

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

Explanation:

The coefficient of $x^{2}$ $x^2$ is $1$ $bb1$ , so the factors will be of this form:

$(x + a) (x + b)$ $(x +a)(x+b)$

We are looking for an $a$ $bba$ and a $b$ $bb(b)$ such that:

$a \times b = - 42$ $axxb=-42$

$a + b = - 1$ $a+b=-1$

Possible factors for $a \times b = - 42$ $a xx b =-42$ are:

$- 1 \times 42$ $-1 xx 42$

$1 \times 42$ $1 xx 42$

$2 \times - 21$ $2xx-21$

$- 2 \times 21$ $-2xx21$

$6 \times - 7$ $6xx-7$

$- 6 \times 7$ $-6xx7$

$3 \times - 14$ $3xx-14$

$- 3 \times 14$ $-3xx14$

The sum has to equal -1.

We can see that the only factors with a sum of $- 1$ $-1$ is $6 and - 7$ $6 and -7$ .

$6 + (- 7) = - 1$ $6+(-7)=-1$

These are the required values:

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

Expanding:

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

As required.

With practice you will quickly find the required values without having to list them all.

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How do you factor the expression $x^{2} - x - 42$ $x^2-x-42$ ?

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How do you factor the expression $x^{2} - x - 42$ $x^2-x-42$ ?