3 Remember Long Division Does 8 go into 6?NoDoes 8 go into 64?Yes, write the integer on top.Multiply 8∙8Write under the dividendSubtract and Carry DownHow many times does 8 go into 7 evenly?0 write over the 7Multiply 0∙8Subtract and write remainder as a fraction.
4 The divisor and quotient are only FACTORS if the remainder is Zero.
9 Long division of polynomials is tedious! Lets learn a simplified process! This process is called Synthetic Divisionp. 316 It may look complicated, but watch a few examples and you will get the hang of it.
10 Use synthetic division to divide 3x3-4x2+2x-1 by x+1 Reverse the sign of the constant term in the divisor. Write the coefficients of the polynomial in standard form (Remember to include zeros)Translation: Instead of writeBring down the first coefficientMultiply the first coefficient by the new divisor. Add.Repeat step 3 until the end. The last number is the remainder.NOW write the polynomial.To write the answer use one less degree than the original polynomial.
11 Example: Use synthetic division to divide x3+4x2+x-6 by x+1x3-2x2-5x+6 by x+2
12 Remainder TheoremIf a polynomial is being divided by (x-a) then the remainder is P(a).Example: Use the remainder theorem to find P(-4) for P(x)=x3-5x2+4x+12DO NOT change the number P(a) to -a
13 Try This ProblemUse synthetic division to find P(-1) for P(x)=4x4+6x3-5x2-60