Factorize the expression x2 - x − 30.

Question

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I will solve question 7(b) from the image.

The question asks to factorize the expression $x^2 - x - 30$ .

Identify the coefficients.
For a quadratic expression in the form $ax^2 + bx + c$ , we have $a=1$ , $b=-1$ , and $c=-30$ .
Find two numbers that multiply to $ac$ and add to $b$ .
Here, $ac = 1 \times (-30) = -30$ . We need two numbers that multiply to $-30$ and add to $-1$ . These numbers are 5 and $-6$ .
Rewrite the middle term using these two numbers.
$x^2 - x - 30 = x^2 + 5x - 6x - 30$
Factor by grouping.
Group the terms and factor out the common factors from each group.
$(x^2 + 5x) - (6x + 30)$
Factor $x$ from the first group and 6 from the second group.
$x(x + 5) - 6(x + 5)$
Factor out the common binomial.
$(x + 5)(x - 6)$
The factored form of $x^2 - x - 30$ is $(x + 5)(x - 6)$ .

Factorize the expression x2 - x - 30.