Question

factor completely
$r^2 - r - 56$
options:
$4(r + 3)(r + 9)$
$(r + 7)(r - 8)$
not factorable
$3(r - 3)(r + 8)$

Explanation:

Step1: Recall factoring quadratic formula

To factor \( r^2 - r - 56 \), we need two numbers that multiply to \( -56 \) and add up to \( -1 \).

Step2: Find the two numbers

Let the numbers be \( a \) and \( b \), so \( a \times b=-56 \) and \( a + b=-1 \). The numbers are \( 7 \) and \( -8 \) because \( 7\times(-8)=-56 \) and \( 7+(-8)=-1 \).

Step3: Factor the quadratic

Using the numbers, we can factor \( r^2 - r - 56 \) as \( (r + 7)(r - 8) \).

Answer:

\((r + 7)(r - 8)\) (corresponding to the purple option: \((r + 7)(r - 8)\))