Dividing Polynomials

3x3 4x2 x 2 1 1 1 1 Dividing by a Monomial If the divisor only has one term, split the polynomial up into a fraction for each term. divisor Now reduce each fraction. 3x3 4x2 x 2 1 1 1 1

Divide without using a calculator.  

Subtract (which changes the sign of each term in the polynomial) Long Division If the divisor has more than one term, perform long division. You do the same steps with polynomial division as with integers. Let's do two problems, one with integers you know how to do and one with polynomials and copy the steps. Subtract (which changes the sign of each term in the polynomial) Now multiply by the divisor and put the answer below. x + 11 2 1 Bring down the next number or term Multiply and put below Now divide 3 into 5 or x into 11x First divide 3 into 6 or x into x2 32 698 x - 3 x2 + 8x - 5 Remainder added here over divisor 64 x2 – 3x subtract 5 8 11x - 5 32 11x - 33 This is the remainder 26 28 So we found the answer to the problem x2 + 8x – 5  x – 3 or the problem written another way:

Remainder added here over divisor Let's Try Another One If any powers of terms are missing you should write them in with zeros in front to keep all of your columns straight. Subtract (which changes the sign of each term in the polynomial) y - 2 Write out with long division including 0y for missing term Multiply and put below Bring down the next term Multiply and put below y + 2 y2 + 0y + 8 Divide y into y2 Divide y into -2y Remainder added here over divisor y2 + 2y subtract -2y + 8 - 2y - 4 This is the remainder 12