Set up division: Set up the long division.We will divide the polynomial (x2−11x+36) by the binomial (x−5) using long division.
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: Multiply the divisor by the first term of the quotient.Multiply (x−5) by x to get x2−5x. Write this below the dividend.
Subtract result: Subtract the result from Step 3 from the dividend.Subtract (x2−5x) from (x2−11x+36) to get −6x+36.
Bring down next term: Bring down the next term of the dividend.There are no more terms to bring down, so we continue with −6x+36.
Divide new first term: Divide the new first term of the remaining dividend by the first term of the divisor.Divide −6x by x to get −6. This will be the next term of the quotient.
Multiply new term: Multiply the divisor by the new term of the quotient.Multiply (x−5) by −6 to get −6x+30. Write this below the remaining dividend.
Subtract result: Subtract the result from Step 7 from the remaining dividend.Subtract (−6x+30) from (−6x+36) to get 6.
Check 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 6. The quotient is x−6 with a remainder of 6.
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