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Answer :
Final answer:
To divide the polynomial (x⁴+11x³+19x²-x-15) by (x+2), you can use polynomial long division.
Explanation:
To divide the polynomial x⁴+11x+19x²-x-15 by x+2, we can use polynomial long division. Here are the steps:
- Divide the first term of the polynomial, x⁴, by the first term of the divisor, x. The quotient is x³.
- Multiply the entire divisor, x+2, by the quotient, x³. The result is x⁴+2x³.
- Subtract the result from the original polynomial. The new polynomial is 9x³+19x²-x-15.
- Repeat the process with the new polynomial. Divide the first term, 9x³, by the first term of the divisor, x. The quotient is 9x².
- Multiply the divisor, x+2, by the quotient, 9x², and subtract the result from the new polynomial.
- Continue the process until there are no more terms left to divide.
The final quotient is x³+9x²-9x-22 and the remainder is -49.
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