Q. Divide the polynomials. Your answer should be in the form p(x)+x−1k where p is a polynomial and k is an integer.x−1x2+6x−4=
Set up long division: Set up the long division.We will use long division to divide the polynomial x2+6x−4 by x−1.
Divide first term: Divide the first term of the dividend by the first term of the divisor. Divide x2 by x to get x. This will be the first term of the quotient.
Multiply divisor and quotient: Multiply the divisor by the first term of the quotient.Multiply x−1 by x to get x2−x.
Subtract result: Subtract the result from the dividend.Subtract x2−x from x2+6x−4 to get 7x−4.
Bring down next term: Bring down the next term. Since there are no more terms to bring down, we proceed to the next step.
Divide new term: Divide the new term by the first term of the divisor.Divide 7x by x to get 7. This will be the next term of the quotient.
Multiply divisor and new term: Multiply the divisor by the new term of the quotient.Multiply x−1 by 7 to get 7x−7.
Subtract result: Subtract the result from the new term of the dividend.Subtract 7x−7 from 7x−4 to get 3.
Check degree of remainder: Since the degree of the remainder (0) is less than the degree of the divisor (1), we cannot continue the division.The remainder is 3, and the quotient is x+7.
Write final answer: Write the final answer in the form p(x)+x−1k.The quotient is x+7 and the remainder is 3, so the final answer is p(x)=x+7 and k=3.
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