Given that the two functions are [tex]f(x)=5x^3-x^2-60x+12[/tex] and [tex]g(x)=5x-1[/tex]
We need to determine the value of [tex]\frac{f(x)}{g(x)}[/tex]
The value of [tex]\frac{f(x)}{g(x)}[/tex]:
To determine the value of [tex]\frac{f(x)}{g(x)}[/tex], let us substitute the functions [tex]f(x)=5x^3-x^2-60x+12[/tex] and [tex]g(x)=5x-1[/tex] in [tex]\frac{f(x)}{g(x)}[/tex]
Thus, we get;
[tex]\frac{f(x)}{g(x)}=\frac{5x^3-x^2-60x+12}{5x-1}[/tex]
Let us group the terms in the numerator.
Thus, we get;
[tex]\frac{f(x)}{g(x)}=\frac{(5x^3-x^2)-(60x-12)}{5x-1}[/tex]
Factoring out the common terms from each group, we get;
[tex]\frac{f(x)}{g(x)}=\frac{x^2(5x-1)-12(5x-1)}{5x-1}[/tex]
Factoring out the term (5x - 1), we have;
[tex]\frac{f(x)}{g(x)}=\frac{(x^2-12)(5x-1)}{5x-1}[/tex]
Cancelling the common terms, we get;
[tex]\frac{f(x)}{g(x)}=x^2-12[/tex]
Thus, the value of [tex]\frac{f(x)}{g(x)}[/tex] is [tex]x^2-12[/tex]
Hence, Option A is the correct answer.
