Final answer:
The process for determining the quotient and remainder for the given polynomials involves multiplying the provided quotient by the divisor and subtracting the result from the original polynomial to find the remainder.
Step-by-step explanation:
The question at hand involves performing polynomial division, to find the quotient and remainder when dividing a second-degree polynomial by a first-degree polynomial. In this case, the polynomial x² - 8x + 15 is to be divided by x - 5. Given that the quotient is x - 3, we can verify it by multiplication and then find the remainder by subtraction.
To illustrate:
- Multiply the given quotient x - 3 by the divisor x - 5.
- Subtract the result from the original polynomial to determine the remainder.
The process resembles long division that is typically done with numbers, and it is useful for simplifying polynomial expressions or solving polynomial equations.