Examples

$x^{2} - 10 x + 25$

Step 1

Find the discriminant for $x^{2} - 10 x + 25 = 0$ . In this case, $b^{2} - 4 a c = 0$ .

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Step 1.1

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

$b^{2} - 4 (a c)$

Step 1.2

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 10)}^{2} - 4 (1 \cdot 25)$

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

Raise $- 10$ to the power of $2$ .

$100 - 4 (1 \cdot 25)$

Step 1.3.1.2

Multiply $- 4 (1 \cdot 25)$ .

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Step 1.3.1.2.1

Multiply $25$ by $1$ .

$100 - 4 \cdot 25$

Step 1.3.1.2.2

Multiply $- 4$ by $25$ .

$100 - 100$

Step 1.3.2

Subtract $100$ from $100$ .

$0$

Step 2

A perfect square number is an integer that is the square of another integer. $\sqrt{0} = 0$ , which is an integer number.

$\sqrt{0} = 0$

Step 3

Since $0$ is the square of $0$ , it is a perfect square number.

$0$ is a perfect square number

Step 4

The polynomial $x^{2} - 10 x + 25$ is not prime because the discriminant is a perfect square number.

Not prime

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