Question

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

Answer 1

Answer:

$f(x) = 2x^2 - x - 1$

$g(x) = 2x + 1$

Step-by-step explanation:

Let the two polynomials be represented with f(x) and g(x);

Since, we have to generate the polynomial ourselves;

I'll make use of the following:

$f(x) = 2x^2 - x - 1$

$g(x) = 2x + 1$

Note that; when the result of polynomial division is referred to as quotient;

To get the quotient, we simply divide f(x) by g(x)

$\frac{f(x)}{g(x)} = \frac{2x^2 - x - 1}{2x + 1}$

Expand the numerator

$\frac{f(x)}{g(x)} = \frac{2x^2 - 2x + x - 1}{2x + 1}$

$\frac{f(x)}{g(x)} = \frac{2x(x - 1) +1(x - 1)}{2x + 1}$

Factorize:

$\frac{f(x)}{g(x)} = \frac{(2x + 1)(x - 1)}{2x + 1}$

Cross out 2x + 1

$\frac{f(x)}{g(x)} = x - 1$

This implies that, the quotient, Q(x) is

$Q(x) = x - 1$

Comparing the divisor g(x) and the quotient Q(x), we notice that they have the same degree of 1