Question

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

Answer 1

Answer:

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

$g(x) = 5x + 2$

Step-by-step 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)

$\frac{f(x)}{g(x)} = \frac{15x^2 -14x - 8}{5x + 2}$

Factorize the numerator

$\frac{f(x)}{g(x)} = \frac{15x^2 - 20x + 6x - 8}{5x + 2}$

$\frac{f(x)}{g(x)} = \frac{(5x + 2)(3x - 4)}{5x + 2}$

Cross out 5x + 2

$\frac{f(x)}{g(x)} = 3x - 4$

The result is referred to as quotient, Q

$Q = 3x - 4$

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