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Q.
- Use polynomial long division: To divide the polynomial by the binomial , we will use polynomial long division.
- Divide leading terms: First, we divide the leading term of the numerator, , by the leading term of the denominator, . This gives us . We then multiply the entire denominator by and subtract the result from the original polynomial.
- Subtract and multiply: Multiplying by gives us . We write this below the original polynomial and subtract..
- Bring down next term: Bring down the next term of the original polynomial to get . Now, divide the leading term of this result, , by the leading term of the denominator, , to get .
- Divide leading terms again: Multiply the entire denominator by and subtract the result from . Multiplying gives us , which we subtract from to get .
- Subtract and multiply: Simplifying gives us . Bring down the next term of the original polynomial to get . Now, divide the leading term of this result, , by the leading term of the denominator, , to get .
- Bring down next term again: Multiply the entire denominator by and subtract the result from . Multiplying gives us , which we subtract from to get the remainder.
- Divide leading terms once more: Simplifying gives us . So, the remainder is , and the quotient we have obtained is .
- Subtract and find remainder: The final answer is the quotient plus the remainder over the original divisor: .
