Determine if Prime x^2-5x+6

$x^{2} - 5 x + 6$

Find the discriminant for $x^{2} - 5 x + 6 = 0$ . In this case, $b^{2} - 4 a c = 1$ .

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 $c$ .

${(- 5)}^{2} - 4 (1 \cdot 6)$

Evaluate the result to find the discriminant.

Simplify each term.

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

$25 - 4 (1 \cdot 6)$

Multiply $6$ by $1$ .

$25 - 4 \cdot 6$

Multiply $- 4$ by $6$ .

$25 - 24$

Subtract $24$ from $25$ .

$1$

A perfect square number is an integer that is the square of another integer. $\sqrt{1} = 1$ , which is an integer number.

$\sqrt{1} = 1$

Since $1$ is the square of $1$ , it is a perfect square number.

$1$ is a perfect square number

The polynomial $x^{2} - 5 x + 6$ is not prime because the discriminant is a perfect square number.

Not prime