Q. Divide the polynomials.The form of your answer should either be p(x) or p(x)+x−4k where p(x) is a polynomial and k is an integer.x−44x3−14x2−7x−4=
Set up long division: Set up the long division.We will use polynomial long division to divide 4x3−14x2−7x−4 by x−4.
Divide first term of dividend: Divide the first term of the dividend by the first term of the divisor.Divide 4x3 by x to get 4x2. Write 4x2 above the dividend.
Multiply divisor and subtract: Multiply the divisor by 4x2 and subtract from the dividend.4x2⋅(x−4)=4x3−16x2. Subtract this from the dividend to get a new dividend of −2x2−7x−4.
Divide first term of new dividend: Divide the first term of the new dividend by the first term of the divisor.Divide −2x2 by x to get −2x. Write −2x above the dividend next to 4x2.
Multiply divisor and subtract: Multiply the divisor by −2x and subtract from the new dividend.−2x⋅(x−4)=−2x2+8x. Subtract this from the new dividend to get a new dividend of −15x−4.
Divide first term of new dividend: Divide the first term of the new dividend by the first term of the divisor.Divide −15x by x to get −15. Write −15 above the dividend next to −2x.
Multiply divisor and subtract: Multiply the divisor by −15 and subtract from the new dividend.−15⋅(x−4)=−15x+60. Subtract this from the new dividend to get a new dividend of −64.
Check for further division: Since −64 is a constant and the divisor is linear, we cannot divide further. The remainder is −64.The division process is complete, and the remainder is −64.
More problems from Composition of linear and quadratic functions: find an equation