Precalculus Examples

$x^{2} - 4 x + 4$

Step 1

Find the discriminant for

$x^{2} - 4 x + 4 = 0$ . In this case,

$b^{2} - 4 a c = 0$ .

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Step 1.1

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

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

Step 1.2

Substitute in the values of

$a$ ,

$b$ , and

$c$ .

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

Step 1.3

Evaluate the result to find the discriminant.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Raise

$- 4$ to the power of

$2$ .

$16 - 4 (1 \cdot 4)$

Step 1.3.1.2

Multiply

$- 4 (1 \cdot 4)$ .

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Step 1.3.1.2.1

Multiply

$4$ by

$1$ .

$16 - 4 \cdot 4$

Step 1.3.1.2.2

Multiply

$- 4$ by

$4$ .

$16 - 16$

Step 1.3.2

Subtract

$16$ from

$16$ .

$0$

Step 2

A perfect square number is an integer that is the square of another integer.

$\sqrt{0} = 0$ , which is an integer number.

$\sqrt{0} = 0$

Step 3

Since

$0$ is the square of

$0$ , it is a perfect square number.

$0$ is a perfect square number

Step 4

The polynomial

$x^{2} - 4 x + 4$ is not prime because the discriminant is a perfect square number.

Not prime

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