Question

Write two polynomial functions whose quotient will be the same degree as the divisor?

Answer 1

`f(x) = 15x^2 -14x - 8`

`g(x) = 5x + 2`

Explanation:

Represent the two polynomials with f(x) and g(x)

The question requires that we assume values for f(x) and g(x) as long as the condition in the question is met;

Let

`f(x) = 15x^2 -14x - 8`

`g(x) = 5x + 2`

To determine if the condition is met, we need to divide f(x) by g(x)

`(f(x))/(g(x)) = (15x^2 -14x - 8)/(5x + 2)`

Factorize the numerator

`(f(x))/(g(x)) = (15x^2 - 20x + 6x - 8)/(5x + 2)`

`(f(x))/(g(x)) = ((5x + 2)(3x - 4))/(5x + 2)`

Cross out 5x + 2

`(f(x))/(g(x)) = 3x - 4`

The result is referred to as quotient, Q

`Q = 3x - 4`

Note that Q and g(x) have the same degree of 1