Q. Divide the polynomials.The form of your answer should either be p(x) or p(x)+x+3k where p(x) is a polynomial and k is an integer.x+32x3−x2−25x−12=
Set up long division: Set up the long division.We will use polynomial long division to divide (2x3−x2−25x−12) by (x+3).
Divide first term: Divide the first term of the dividend by the first term of the divisor.Divide 2x3 by x to get 2x2.Write 2x2 above the division bar.
Multiply divisor and result: Multiply the divisor (x+3) by the result from Step 2(2x2).2x2∗(x+3)=2x3+6x2.
Subtract result from dividend: Subtract the result from Step 3 from the dividend.(2x3−x2−25x−12)−(2x3+6x2)=−7x2−25x−12.
Bring down next term: Bring down the next term of the dividend to prepare for the next division step.We now have −7x2−25x.
Divide first term of new dividend: Divide the first term of the new dividend by the first term of the divisor.Divide −7x2 by x to get −7x.Write −7x above the division bar, next to 2x2.
Multiply divisor and result: Multiply the divisor (x+3) by the result from Step 6(−7x).−7x×(x+3)=−7x2−21x.
Subtract result from new dividend: Subtract the result from Step 7 from the new dividend.(−7x2−25x)−(−7x2−21x)=−4x.
Bring down next term: Bring down the next term of the dividend to prepare for the next division step.We now have −4x−12.
Divide first term of new dividend: Divide the first term of the new dividend by the first term of the divisor.Divide −4x by x to get −4.Write −4 above the division bar, next to 2x2−7x.
Multiply divisor and result: Multiply the divisor (x+3) by the result from Step 10(−4).−4×(x+3)=−4x−12.
Subtract result from new dividend: Subtract the result from Step 11 from the new dividend.(−4x−12)−(−4x−12)=0.
Write final answer: Write the final answer.Since there is no remainder, the result of the division is the polynomial written above the division bar: 2x2−7x−4.
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