Question: Factor the trinomial. \[ r^2 + 18r + 80 \] Select the correct choice below and, if necessary,…

Factor the trinomial.

\[ r^2 + 18r + 80 \]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. \( r^2 + 18r + 80 = \boxed{\phantom{0}} \) (Factor completely.)

B. The polynomial is prime.

Solution

To factor the trinomial \( r^2 + 18r + 80 \), follow these steps: First, find two numbers that multiply to \( 80 \) and add to \( 18 \). The numbers \( 10 \) and \( 8 \) work because \[ 10 \times 8 = 80 \] and \[ 10 + 8 = 18 \] Now, use these numbers to factor the trinomial: \[ r^2 + 18r + 80 = (r + 10)(r + 8) \] Thus, the factored form is \((r + 10)(r + 8)\).