Algebra Examples

$3 x^{2} + x - 6 x - 2$

Step 1

Find the discriminant for $3 x^{2} + x - 6 x - 2 = 0$ . In this case, $b^{2} - 4 a c = 49$ .

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Step 1.1

Simplify the left side.

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Step 1.1.1

Subtract $6 x$ from $x$ .

$3 x^{2} - 5 x - 2 = 0$

Step 1.2

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

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

Step 1.3

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

${(- 5)}^{2} - 4 (3 \cdot - 2)$

Step 1.4

Evaluate the result to find the discriminant.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Raise $- 5$ to the power of $2$ .

$25 - 4 (3 \cdot - 2)$

Step 1.4.1.2

Multiply $- 4 (3 \cdot - 2)$ .

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Step 1.4.1.2.1

Multiply $3$ by $- 2$ .

$25 - 4 \cdot - 6$

Step 1.4.1.2.2

Multiply $- 4$ by $- 6$ .

$25 + 24$

Step 1.4.2

Add $25$ and $24$ .

$49$

Step 2

A perfect square number is an integer that is the square of another integer. $\sqrt{49} = 7$ , which is an integer number.

$\sqrt{49} = 7$

Step 3

Since $49$ is the square of $7$ , it is a perfect square number.

$49$ is a perfect square number

Step 4

The polynomial $3 x^{2} + x - 6 x - 2$ is not prime because the discriminant is a perfect square number.

Not prime