(y^2 - y + 2)/(y + 2)
I put this in calc101 . com and I got an answer with y - 3 in the quotient and got 8 in thr remainder area. My answer key says the answer is y - 3 + 8/y + 2. Can someone explain how the answer key has this answer?
sure
(5) /2 = 2 Remainder 1
which is exactly the same as
2 1/2
That is really what "remainder means" .
To understand how the answer key obtained the answer y - 3 + 8/(y + 2), let's break down the process step by step.
First, we need to perform polynomial long division to divide the numerator (y^2 - y + 2) by the denominator (y + 2). Here's how it works:
1. Start by writing the division problem in long division format:
________________________
y + 2 | y^2 - y + 2
2. Divide the first term of the numerator (y^2) by the first term of the denominator (y). The result is y, which becomes the first term in the quotient:
y
________________________
y + 2 | y^2 - y + 2
3. Multiply the entire denominator (y + 2) by the quotient's first term (y). Write the result below the numerator, and subtract it from the original numerator:
y
________________________
y + 2 | y^2 - y + 2
- (y^2 + 2y)
_____________
- 3y + 2
4. Bring down the next term of the numerator (-3y) and perform the division again:
y - 3
________________________
y + 2 | y^2 - y + 2
- (y^2 + 2y)
_____________
- 3y + 2
- (- 3y - 6)
_______________
8
5. The remainder of the division is 8. Hence, the final answer is y - 3 + 8/(y + 2).
Therefore, your answer key's solution of y - 3 + 8/(y + 2) is correct based on the polynomial long division process.