Question

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

$n^2-\mathbf{16}$

Short answer

The factors $n^2-16$ are $\left(n+4\right)\left(n-4\right)$.

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 $a^2-b^2$.

$n^2-4^2$

Step 3. Factor the difference of squares.

Factors the difference of squares, that is, $n^2-4^2$.

$\left(n+4\right)\left(n-4\right)$.

Therefore, the factors of $n^2-16$are $\left(n+4\right)\left(n-4\right)$.