(Solved):Divide and check using long division. dfrac{x^2-32}{x – 8} View Answer…

 

Question

Divide and check using long division.

$$dfrac{x^2-32}{x – 8}

$$

 

EXPERT ANSWER

Expression:

{eq}frac{x^2-32}{x-8}

{/eq}

We need to use a term that multiplied by {eq}x-8

{/eq} give us an expression useful to eliminate the first term of the numerator, this term is: {eq}x

{/eq}. If we multiply this term by {eq}x-8

{/eq} we have this: {eq}x cdot left(x-8right)=x^2-8x

{/eq}. Then, we need to subtract the numerator and the last expression: {eq}x^2-32-left(x^2-8xright)=8x-32

{/eq}.

Now we have this new expression:

{eq}x+frac{8x-32}{x-8} quad textrm{The first term

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