Question

Rewrite c(x) = (x ² 5x 2)/(x - 3) in the form y = q(x) (r(x))/(b(x)) has degree less than b.

Options:
A. q(x)=x,r(x)=x² −5x+2,b(x)=x−3
B. q(x)=x² −5x+2,r(x)=x,b(x)=x−3
C. q(x)=x² −5x+2,r(x)=1,b(x)=x−3
D. q(x)=x,r(x)=1,b(x)=x² −5x+2

Answer 1

The correct answer is option A: q(x)=x, r(x)=x² −5x+2, b(x)=x−3. In this case, there seems to be a typo in the question since r(x) does not have a degree less than b(x), but option A accurately reflects the original function.

Step-by-step explanation:

The question asks to rewrite the function c(x) = (x² + 5x + 2) / (x - 3) in the form y = q(x) (r(x)) / (b(x)) where r(x) has degree less than b(x).

Out of the given options, the correct answer is:
A. q(x)=x, r(x)=x² −5x+2, b(x)=x−3
because when we factor c(x), we can see that there is no polynomial with a degree lower than the denominator polynomial that can be split off. The question may contain a typo, since normally for a proper rational function, r(x)'s degree should be less than b(x)'s degree. However, following the provided options, option A is the only one that represents the original function accurately without changing its meaning or value.