Question: Factor the polynomial. $$196r^2 + 225$$ Select the correct choice below and, if necessary, fill…

Factor the polynomial.

$$196r^2 + 225$$

Select the correct choice below and, if necessary, fill in the answer.

A. $$196r^2 + 225 = \boxed{\phantom{0}}$$

(Factor completely.)

B. The polynomial is prime.

Solution

Step 1 Determine if the polynomial can be factored. Step 2 Recognize that \( 196r^2 + 225 \) is a sum of squares: \[ 196r^2 + 225 = (14r)^2 + 15^2 \] Step 3 Recall that the sum of squares cannot be factored into real linear factors. Step 4 Conclude that the polynomial is prime. Answer: B. The polynomial is prime.