Question

which of the following expressions is equivalent to $x^2 - x - 30$?

• $(x + 3)(x - 10)$
• $(x + 6)(x - 5)$
• $(x - 6)(x + 5)$
• $(x - 15)(x - 15)$

Explanation:

Step1: Recall factoring quadratic

We need to factor \(x^2 - x - 30\). We look for two numbers that multiply to \(-30\) and add to \(-1\).

Step2: Find the numbers

The numbers are \(-6\) and \(5\) because \(-6\times5 = -30\) and \(-6 + 5=-1\).

Step3: Write the factored form

So, \(x^2 - x - 30=(x - 6)(x + 5)\) (we can also check by expanding each option:

• Expand \((x + 3)(x - 10)=x^2-10x + 3x-30=x^2 - 7x - 30\) (not equal)
• Expand \((x + 6)(x - 5)=x^2-5x + 6x-30=x^2 + x - 30\) (not equal)
• Expand \((x - 6)(x + 5)=x^2+5x - 6x-30=x^2 - x - 30\) (equal)
• Expand \((x - 15)(x - 15)=x^2-30x + 225\) (not equal)

Answer:

\((x - 6)(x + 5)\) (the third option)