Question

value: 3
factor completely
$r^2 - 7r - 18$
\\(\circ\\) a. \\((r - 2)(r - 1)\\)
\\(\circ\\) b. \\((r - 9)(r - 2)\\)
\\(\circ\\) c. \\((r + 9)(r - 2)\\)
\\(\circ\\) d. \\((r - 9)(r + 2)\\)

Explanation:

Step1: Find pair for sum -7, product -18

We need two numbers that add to $-7$ and multiply to $-18$. The numbers are $-9$ and $2$, since $-9 + 2 = -7$ and $-9 \times 2 = -18$.

Step2: Split middle term and factor

Rewrite the quadratic: $r^2 -9r +2r -18$
Group and factor: $r(r-9) + 2(r-9) = (r-9)(r+2)$

Answer:

d. $(r-9)(r+2)$