Question

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

Answer 1

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.