Question

Write two polynomial functions whose quotients will have a degree of zero.

Answer 1

Answer:

$\begin{gathered} f(x)=6x^2+4x+2 \\ g(x_{})=18x^2+12x+6 \end{gathered}$

Explanation:

Definition:

The degree of a polynomial is the highest index/power of the variable in the polynomial.

The quotient of two polynomials will have a degree of zero if they are multiples of one another.

Let the two polynomial functions be:

$\begin{gathered} f(x)=6x^2+4x+2 \\ g(x_{})=18x^2+12x+6 \end{gathered}$

Its quotient:

$\begin{gathered} \frac{f(x)}{g(x)}=\frac{6x^2+4x+2}{18x^2+12x+6} \\ =\frac{2(3x^2+2x+1)}{6(3x^2+2x+1)} \\ =\frac{2}{6} \\ =\frac{1}{3} \end{gathered}$

Note:

$\frac{1}{3}=\frac{1}{3}x^0$

Since the quotient is a constant, it has a degree of zero.