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 box to complete your choice.

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

B. The polynomial is prime.

Solution

The problem is to factor the polynomial \(196x^2 + 225\). First, recognize that this polynomial is a sum of squares: \[ 196x^2 = (14x)^2 \] \[ 225 = 15^2 \] The expression can be factored using the sum of squares formula: \[ a^2 + b^2 = (a + bi)(a - bi) \] In this case: \[ a = 14x, \quad b = 15 \] Substitute these values into the formula: \[ (14x + 15i)(14x - 15i) \] So, the factorization of \(196x^2 + 225\) is \((14x + 15i)(14x - 15i)\).