Precalculus Examples

$x^{2} + 2 x - 1$

Step 1

Find the discriminant for $x^{2} + 2 x - 1 = 0$ . In this case, $b^{2} - 4 a c = 8$ .

Tap for more steps...

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 $c$ .

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

Step 1.3

Evaluate the result to find the discriminant.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

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

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

Step 1.3.1.2

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

Tap for more steps...

Step 1.3.1.2.1

Multiply $- 1$ by $1$ .

$4 - 4 \cdot - 1$

Step 1.3.1.2.2

Multiply $- 4$ by $- 1$ .

$4 + 4$

Step 1.3.2

Add $4$ and $4$ .

$8$

Step 2

A perfect square number is an integer that is the square of another integer. $\sqrt{8} \approx 2.82842712$ , which is not an integer number.

$\sqrt{8} \approx 2.82842712$

Step 3

Since $8$ can't be the square of another integer, it is not a perfect square number.

Step 4

The polynomial $x^{2} + 2 x - 1$ is prime because the discriminant is not a perfect square number.

Prime