Q83. - Algebra 1

Question

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

$x^2+\mathbf{25}$

Step-by-Step Solution

Answer

$x^2+25$ is a prime.

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 a 2 − b 2 .

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.