Synthetic Division

Review: What is a polynomial? How do we know the degree of the polynomial?

Division We have looked at addition, subtraction and multiplication of polynomials Division of polynomials is slightly different

Synthetic Division Division of polynomials is similar to long division There is a shorter method Called synthetic division

When to use synthetic division When the divisor is a first degree polynomial such as x-2 or x+5 Caution: Synthetic division can be used only when the divisor is x-c So what do you do if it is x+c? Write in form x-(-c)

Synthetic Division Steps Setup as shown below Be sure to write out each degree If it is not in the problem, include it as a 0x

Steps in Synthetic Division Step 1: In the first row, write the constant from the divisor and the coefficients of the dividend in order of decreasing powers of x Insert 0 for missing powers of x Step 2: Skip a line, draw a line, and draw a partial box under the line beneath the last coefficient in the first row

Step 3: Bring the first coefficient of the dividend below the line Step 4: Multiply the divisor constant and the number below the line. Step 5: Place the product, under the dividend’s next coefficient Step 6: Add the numbers in that column and write the sum below the column under the line

Repeat going the whole way across the row, stopping when you put the number in the box at the end The last number in the third row is the remainder. The other numbers in the third row are the coefficients of the quotient, arranged in order of decreasing powers of x. Write them out from right to left

Divide 3x 4 -8x 2 -11x+1 by x- 2

Divide x 5 +5x 4 +6x 3 - x 2 +4x+29 by x+3

Divide 3x 4 -8x 3 +9x+5 by x- 2

Divide 2x 4 +5x 3 -2x-8 by x+3