Determine if the Given Expression is a Factor

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

Step 1

If $x - 2$ is a factor of the polynomial, then it must be a root of the polynomial. To determine if the factor is a root, first find the value of $x$ when the factor $x - 2$ is equal to $0$ .

$x - 2 = 0$

Step 2

Solve the equation for $x$ .

$x = 2$

Step 3

Replace $x$ with $2$ in $x^{2} - 4$ to find if it is a root of the polynomial.

${(2)}^{2} - 4$

Step 4

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

$4 - 4$

Step 5

Subtract $4$ from $4$ .

$0$

Step 6

Since $x = 2$ is a root of the polynomial, $x - 2$ is a factor of the polynomial.

$x - 2$ is a factor of $x^{2} - 4$

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Factoring Polynomials

More step-by-step Precalculus examples from this chapter.

Finding the GCF of a Polynomial Factoring Out Greatest Common Factor (GCF) Identifying the Common Factors Cancelling the Common Factors Factoring Trinomials Trinomial Squares Factoring Using Any Method Factoring a Difference of Squares Factoring a Sum of Cubes Factoring by Grouping Factoring a Difference of Cubes Determining if Factor Using Synthetic Division

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$