Final answer:
The question requires simplifying a polynomial division ((3x^2-8x+7) divided by (x-1)). It involves finding the quotient using polynomial long division and verifying the answer.
Step-by-step explanation:
The student's question involves the simplification of a rational algebraic expression. The process to simplify the algebra involves performing polynomial division. The division of the polynomial (3x2 - 8x + 7) by (x - 1) needs to be carried out to find the quotient.
Here are the steps for simplifying the expression:
- Divide the first term of the numerator by the first term of the denominator and write the result above the division bar.
- Multiply the entire denominator by this result and subtract from the numerator.
- Repeat the process with the new polynomial that is now your numerator.
- Continue this process until the degree of the remainder is less than the degree of the divisor.
- The result will be the quotient plus the remainder over the original divisor.
- Check the answer to ensure that all signs are correct and the terms have been simplified properly.
It is important that students eliminate terms wherever possible to simplify their expressions and always review their answers to confirm their results are reasonable.