Determine if Prime w^2+4w-5

$w^{2} + 4 w - 5$

Step 1

Find the discriminant for $w^{2} + 4 w - 5 = 0$ . In this case, $b^{2} - 4 a c = 36$ .

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

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

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

$4^{2} - 4 (1 \cdot - 5)$

Evaluate the result to find the discriminant.

Simplify each term.

Raise $4$ to the power of $2$ .

$16 - 4 (1 \cdot - 5)$

Multiply $- 4 (1 \cdot - 5)$ .

Multiply $- 5$ by $1$ .

$16 - 4 \cdot - 5$

Multiply $- 4$ by $- 5$ .

$16 + 20$

Add $16$ and $20$ .

$36$

Step 2

A perfect square number is an integer that is the square of another integer. $\sqrt{36} = 6$ , which is an integer number.

$\sqrt{36} = 6$

Step 3

Since $36$ is the square of $6$ , it is a perfect square number.

$36$ is a perfect square number

Step 4

The polynomial $w^{2} + 4 w - 5$ is not prime because the discriminant is a perfect square number.

Not prime