Question

When the function f(x) is divided by x + 1, the quotient is 3x^2 – 9x – 2 and theremainder is 7. Find the function f(x)

Answer 1

Given:

`(f(x))/(x+1)=3x^2-9x-2+(7)/(x+1)`

To get the function f(x),

We can use the comparison of converting mixed numbers to an improper fraction as shown below;

`a(b)/(x)=((a* x)+b)/(x)`

Hence, following this conversion above,

`\begin{gathered} (f(x))/(x+1)=((3x^2-9x-2)(x+1)+7)/(x+1) \\ (f(x))/(x+1)=((3x^3-9x^2-2x+3x^2-9x-2)+7)/(x+1) \\ (f(x))/(x+1)=((3x^3-9x^2+3x^2-2x-9x-2)+7)/(x+1) \\ (f(x))/(x+1)=((3x^3-6x^2-11x-2)+7)/(x+1) \\ (f(x))/(x+1)=(3x^3-6x^2-11x-2+7)/(x+1) \\ (f(x))/(x+1)=(3x^3-6x^2-11x+5)/(x+1) \\ \\ \text{Comparing both sides of the equation, then } \\ f(x)=3x^3-6x^2-11x+5 \end{gathered}`

Therefore, the function f(x) is;

`3x^3-6x^2-11x+5`