Determine if Prime 10x^2-10x+6x-6

$10 x^{2} - 10 x + 6 x - 6$

Step 1

Find the discriminant for $10 x^{2} - 10 x + 6 x - 6 = 0$ . In this case, $b^{2} - 4 a c = 256$ .

Simplify the left side.

Add $- 10 x$ and $6 x$ .

$10 x^{2} - 4 x - 6 = 0$

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 $c$ .

${(- 4)}^{2} - 4 (10 \cdot - 6)$

Evaluate the result to find the discriminant.

Simplify each term.

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

$16 - 4 (10 \cdot - 6)$

Multiply $- 4 (10 \cdot - 6)$ .

Multiply $10$ by $- 6$ .

$16 - 4 \cdot - 60$

Multiply $- 4$ by $- 60$ .

$16 + 240$

Add $16$ and $240$ .

$256$

Step 2

A perfect square number is an integer that is the square of another integer. $\sqrt{256} = 16$ , which is an integer number.

$\sqrt{256} = 16$

Step 3

Since $256$ is the square of $16$ , it is a perfect square number.

$256$ is a perfect square number

Step 4

The polynomial $10 x^{2} - 10 x + 6 x - 6$ is not prime because the discriminant is a perfect square number.

Not prime