Algebra Examples

Step 1
Find the discriminant for . In this case, .
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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.
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Step 1.3.1
Simplify each term.
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Step 1.3.1.1
Raising to any positive power yields .
Step 1.3.1.2
Multiply .
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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 not an integer number.
Step 3
Since can't be the square of another integer, it is not a perfect square number.
Step 4
The polynomial is prime because the discriminant is not a perfect square number.
Prime
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