Final answer:
The answer involves dividing the polynomial (-7q³+17q²-11q+16) by the binomial (q-2), a task typically done using polynomial long division or synthetic division, which is a high school-level algebra topic.
Step-by-step explanation:
The question involves dividing polynomials, a concept in algebra which is part of high school mathematics curriculum. We are given a polynomial (-7q³+17q²-11q+16) and asked to divide it by the binomial (q-2). The division can be carried out using either polynomial long division or synthetic division.
To divide the polynomial (-7q³+17q²-11q+16) by (q-2), we set up the long division:
- Divide the first term of the numerator by the first term of the denominator: -7q³/q = -7q².
- Multiply the divisor by this quotient and subtract the result from the original polynomial.
- Bring down the next term of the polynomial and repeat the process until all terms have been brought down and the remainder, if any, is less than the degree of the divisor.
After each step, eliminate terms wherever possible to simplify the algebra.
Always check the answer to see if it is reasonable which means ensuring that the product of the divisor and the quotient plus the remainder gives back the original polynomial.