# Precalculus Examples

Step 1

Step 1.1

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

Step 1.2

Substitute in the values of , , and .

Step 1.3

Evaluate the result to find the discriminant.

Step 1.3.1

Simplify each term.

Step 1.3.1.1

Raising to any positive power yields .

Step 1.3.1.2

Multiply .

Step 1.3.1.2.1

Multiply by .

Step 1.3.1.2.2

Multiply by .

Step 1.3.2

Add and .

Step 2

A perfect square number is an integer that is the square of another integer. , which is an integer number.

Step 3

Since is the square of , it is a perfect square number.

is a perfect square number

Step 4

The polynomial is not prime because the discriminant is a perfect square number.

Not prime