Mathematics: Help! Let f(x) = 5x3 − x2 − 60x + 12 and g(x) = 5x − 1. Find f of x over g of x. A. 2 − 12 B. 5x2 + 4x C. x2 − 12x D. 5x2 + 4

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Help! Let f(x) = 5x3 − x2 − 60x + 12 and g(x)

antoniaannswiney

21.01.2022

Given that the two functions are f(x)=5x^3-x^2-60x+12 and g(x)=5x-1

We need to determine the value of $\frac{f(x)}{g(x)}$

The value of $\frac{f(x)}{g(x)}$ :

To determine the value of $\frac{f(x)}{g(x)}$ , let us substitute the functions f(x)=5x^3-x^2-60x+12 and g(x)=5x-1 in $\frac{f(x)}{g(x)}$

Thus, we get;

$\frac{f(x)}{g(x)}=\frac{5x^3-x^2-60x+12}{5x-1}$

Let us group the terms in the numerator.

Thus, we get;

$\frac{f(x)}{g(x)}=\frac{(5x^3-x^2)-(60x-12)}{5x-1}$

Factoring out the common terms from each group, we get;

$\frac{f(x)}{g(x)}=\frac{x^2(5x-1)-12(5x-1)}{5x-1}$

Factoring out the term (5x - 1), we have;

$\frac{f(x)}{g(x)}=\frac{(x^2-12)(5x-1)}{5x-1}$

Cancelling the common terms, we get;

$\frac{f(x)}{g(x)}=x^2-12$

Thus, the value of $\frac{f(x)}{g(x)}$ is x^2-12

Hence, Option A is the correct answer.

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