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Divide. If there is a remainder, include it as a simplified fraction.
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Q. Divide. If there is a remainder, include it as a simplified fraction.
- Given Polynomial and Binomial: We are given the polynomial and we need to divide it by the binomial . We will use polynomial long division to solve this problem.
- Dividing Leading Terms: First, we divide the leading term of the polynomial, , by the leading term of the binomial, . This gives us , because .
- Multiplying and Subtracting: Next, we multiply the divisor by the quotient we just found and subtract the result from the original polynomial. This gives us:.
- Subtracting Result: Performing the subtraction, we get: egin{equation}(y^ + y + ) - (y^ + y) = (y^ - y^) + (y - y) + = y + .egin{equation}
- Dividing New Leading Term: Now, we divide the new leading term, , by the leading term of the binomial, . This gives us , because .
- Multiplying and Subtracting: We multiply the divisor by the new quotient and subtract the result from the remaining polynomial. This gives us:.
- Subtracting Result: Performing the subtraction, we get:.
- Exact Division: Since the remainder is , we do not have a remainder to express as a fraction. The division is exact.
