Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 10, 2024

Divide the polynomial $\left(x^{2}-4\right)$ by $(x-2)$ using factoring.

STEP 1

Assumptions
1. We are given a polynomial $x^{2}-4$ .
2. We are asked to divide this polynomial by $x-2$ .
3. We will use factoring to simplify the division.

STEP 2

Recognize that the polynomial $x^{2}-4$ is a difference of squares, which can be factored into the product of two binomials.
$x^{2}-4 = (x+2)(x-2)$

STEP 3

Now that we have factored the polynomial, we can set up the division.
$\frac{x^{2}-4}{x-2} = \frac{(x+2)(x-2)}{x-2}$

STEP 4

Observe that the $(x-2)$ terms in the numerator and the denominator are identical and can be canceled out.
$\frac{(x+2)(x-2)}{x-2} = x+2$

STEP 5

After canceling, we are left with the simplified result of the division.
$\frac{x^{2}-4}{x-2} = x+2$
The result of the division is $x+2$ .

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