Algebra Examples

$x^{2} - 12$

Step 1

Find the discriminant for $x^{2} - 12 = 0$ . In this case, $b^{2} - 4 a c = 48$ .

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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 $c$ .

$0^{2} - 4 (1 \cdot - 12)$

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 $0$ to any positive power yields $0$ .

$0 - 4 (1 \cdot - 12)$

Step 1.3.1.2

Multiply $- 4 (1 \cdot - 12)$ .

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Step 1.3.1.2.1

Multiply $- 12$ by $1$ .

$0 - 4 \cdot - 12$

Step 1.3.1.2.2

Multiply $- 4$ by $- 12$ .

$0 + 48$

Step 1.3.2

Add $0$ and $48$ .

$48$

Step 2

A perfect square number is an integer that is the square of another integer. $\sqrt{48} \approx 6.92820323$ , which is not an integer number.

$\sqrt{48} \approx 6.92820323$

Step 3

Since $48$ can't be the square of another integer, it is not a perfect square number.

Step 4

The polynomial $x^{2} - 12$ is prime because the discriminant is not a perfect square number.

Prime

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