Answer:
[tex]f(x) = 15x^2 -14x - 8[/tex]
[tex]g(x) = 5x + 2[/tex]
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
[tex]f(x) = 15x^2 -14x - 8[/tex]
[tex]g(x) = 5x + 2[/tex]
To determine if the condition is met, we need to divide f(x) by g(x)
[tex]\frac{f(x)}{g(x)} = \frac{15x^2 -14x - 8}{5x + 2}[/tex]
Factorize the numerator
[tex]\frac{f(x)}{g(x)} = \frac{15x^2 - 20x + 6x - 8}{5x + 2}[/tex]
[tex]\frac{f(x)}{g(x)} = \frac{(5x + 2)(3x - 4)}{5x + 2}[/tex]
Cross out 5x + 2
[tex]\frac{f(x)}{g(x)} = 3x - 4[/tex]
The result is referred to as quotient, Q
[tex]Q = 3x - 4[/tex]
Note that Q and g(x) have the same degree of 1
