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Can I get some help with this because I don't understand how to do this?

Can I get some help with this because I don't understand how to do this?-example-1

1 Answer

4 votes

Given the functions


\begin{gathered} f(x)=x^2+4x-21 \\ g(x)\text{ = x-3} \end{gathered}

To divide f(x) by g(x) implies


(f(x))/(g(x))=(f)/(g)(x)=(x^2+4x-21)/(x-3)

Step 1

Factorize the numerator f(x)


\begin{gathered} x^2+4x-21 \\ \Rightarrow x^2+7x-3x-21 \\ x(x+7)-3(x+7) \\ \Rightarrow(x-3)(x+7) \end{gathered}

Step 2

Divide the factorized numerator by the denominator


\begin{gathered} (f(x))/(g(x))=((x-3)(x+7))/((x-3)) \\ \Rightarrow(f)/(g)(x)\text{ =}x+7 \end{gathered}

Thus,


(f)/(g)(x)\text{ = x+7},\text{ x}\\e3

The second option is the correct answer.

User Alex Markman
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