Question: Factor the trinomial completely. \[ 25x^4 + 40x^2 + 7 \] Select the correct choice below and,…

Factor the trinomial completely.

\[ 25x^4 + 40x^2 + 7 \]

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

A. \( 25x^4 + 40x^2 + 7 = \boxed{\phantom{0}} \) (Factor completely.)

B. The polynomial is prime.

Solution

Let’s solve the problem step by step. \[ y = x^2 \] Substitute \( y \) into the original equation: \[ 25y^2 + 40y + 7 \] Factor the quadratic expression: \[ (5y + 1)(5y + 7) \] Substitute back \( y = x^2 \): \[ (5x^2 + 1)(5x^2 + 7) \] The correct choice is: A. \( 25x^4 + 40x^2 + 7 = (5x^2 + 1)(5x^2 + 7) \)