Question

question 5 of 7
which of the following expressions is equivalent to
$x^2 - x - 30$?
$\bigcirc\\ (x + 3)(x - 10)$
$\bigcirc\\ (x + 6)(x - 5)$
$\bigcirc\\ (x - 6)(x + 5)$
$\bigcirc\\ (x - 15)(x - 15)$

Explanation:

Step1: Recall factoring trinomials

To factor \(x^2 - x - 30\), we need two numbers that multiply to \(-30\) and add to \(-1\).

Step2: Find the two numbers

Let the numbers be \(a\) and \(b\) such that \(a\times b=-30\) and \(a + b=-1\). The numbers are \(-6\) and \(5\) because \((-6)\times5=-30\) and \(-6 + 5=-1\).

Step3: Factor the trinomial

So, \(x^2 - x - 30=(x - 6)(x + 5)\). We can also expand the options to check:

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

Answer:

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