Synthetic DivisionAlgebra 2 CP

Synthetic Division A trick for dividing polynomials Helps us solve for the roots of polynomials Only works when we divide by 1st degree

(linear) polynomials

)2()11183( 24 xxxxExponent can’t be larger than 1!

Synthetic Division

)24()1152( 24 xxxx

)2()11183( 24 xxxx

Your Turn On your Synthetic Division Notes packet,

complete problems 1 – 5. Decide if it’s possible to use synthetic division to

divide the two polynomials

1. Yes 2. Yes 3. No 4. No 5. No

Division Vocab Review

Dividend Divisor

2)3()65( 2 xxxx

Quotient

Preparing for Synthetic Division Can only be used when the divisor is in the

form:

To divide, you will need the constant term of your divisor: set your divisor equal to 0 and solve!

x – c

Preparing for Synthetic Division, cont. Polynomials need to be written in expanded,

standard polynomial form. For the polynomial to be expanded sequentially,

ALL terms must be listed AKA: If you’re missing terms, they must be filled in

with “place holders.”

Preparing for Synthetic Division, cont.

xxx 273 35

xxx 273 35

020703 2345 xxxxx

Your Turn On your Synthetic Division Notes packet, write

the dividend in expanded standard polynomial form for problems 6 – 10.

6.

7.

8.

9.

10.

*Synthetic Division Steps Example Problem:

)2()11183( 24 xxxx

Prep Step Linear Divisor?

x – 2 Dividend in Expanded Standard Polynomial

Form? 3x4 – 8x2 – 11x + 1 3x4 + – 8x2 – 11x + 1 3x4 + 0x3 – 8x2 – 11x + 1

Step 12

Write the constant value of the divisor (c) here.

Step 22

Write all the coefficients of the expanded dividend here.

3 0 -8 -11 1

Step 32

“Drop” the 1st coefficient underneath the line.

3 0 -8 -11 1

3

Step 42

Multiply “c” by the last value underneath the line. Write their product just underneath the next coefficient.

3 0 -8 -11 1

6

3

Step 52

Add together the numbers in that column and write their sum underneath the line.

3 0 -8 -11 1

6

3 6

Step 62

Multiply “c” by the last value underneath the line. Write their product just underneath the next coefficient.

3 0 -8 -11 1

6 12

3 6

Step 72

Repeat steps 5 and 6 until a number appears in the box underneath the last column.

3 0 -8 -11 1

6 12 8 -6

3 6 4 -3 -5

Step 8 – Naming the Quotient2

In the last row are the coefficients of the quotient in decreasing order. The quotient is one degree less than the dividend.

3 0 -8 -11 1

6 12 8 -6

3 6 4 -3 -5

Step 8 – Naming the Quotient3 6 4 -3 -5

The number in the box is the remainder. )2()11183( 24 xxxx

Your Turn On your Synthetic Division Notes packet,

solve for the quotient of problems 11 – 14 using synthetic division

11.

12.

13.

14.