Question

Given that f(x) = x^2 - 8x + 12 and g(x) = x – 6, find (f ÷ g)(x) and express the result in standard form.

Answer 1

`\begin{gathered} f(x)=x^2-8x+12 \\ g(x)=x-6_{} \end{gathered}`

f(x) can be factorized with help of the quadratic formula, as follows:

`\begin{gathered} x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_(1,2)=\frac{-(-8)\pm\sqrt[]{(-8)^2-4\cdot1\cdot12}}{2\cdot1} \\ x_(1,2)=\frac{8\pm\sqrt[]{64-48}}{2} \\ x_(1,2)=(8\pm4)/(2) \\ x_1=(8+4)/(2)=6 \\ x_2=(8-4)/(2)=2 \end{gathered}`

Then, f(x) can be expressed as: (x - 6)(x - 2). Replacing this into (f ÷ g)(x), we get:

`(f\mleft(x\mright))/(g(x))=(x^2-8x+12)/(x-6)=((x-6)(x-2))/(x-6)=x-2`