Determine if Prime 3a^2-10a-32

$3 a^{2} - 10 a - 32$

Find the discriminant for $3 a^{2} - 10 a - 32 = 0$ . In this case, $b^{2} - 4 a c = 484$ .

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 $c$ .

${(- 10)}^{2} - 4 (3 \cdot - 32)$

Evaluate the result to find the discriminant.

Simplify each term.

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

$100 - 4 (3 \cdot - 32)$

Multiply $3$ by $- 32$ .

$100 - 4 \cdot - 96$

Multiply $- 4$ by $- 96$ .

$100 + 384$

Add $100$ and $384$ .

$484$

A perfect square number is an integer that is the square of another integer. $\sqrt{484} = 22$ , which is an integer number.

$\sqrt{484} = 22$

Since $484$ is the square of $22$ , it is a perfect square number.

$484$ is a perfect square number

The polynomial $3 a^{2} - 10 a - 32$ is not prime because the discriminant is a perfect square number.

Not prime