Question

Factor each polynomial if possible. If the polynomial cannot be factored, write prime.

$x^2+\mathbf{25}$

Short answer

$x^2+25$is aprime.

Step-by-step solution

Step 1. Write the property of the product of sum and difference.

The product of $a+b$and $a-b$ is the square of a the minus square of b, that is,

$\left(a+b\right)\left(a-b\right)=a^2-b^2$

Step 2. Write in terms of a2−b2.

Write the given polynomial in terms of $a^2-b^2$.

$x^2+25$cannot be written in the form of $a^2-b^2$.

Step 3. Write the conclusion.

As $x^2+25$ cannot be written in the form of $a^2-b^2$, it cannot be factored and therefore, the given polynomial is prime.