# Synthetic Division Notes

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### Synthetic Division Notes

• 2. 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 −÷+−− xxxx Exponent can’t be larger than 1!
• 3. Synthetic Division )24()1152( 24 −−÷−+ xxxx )2()11183( 24 −÷+−− xxxx
• 4. 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
• 5. Division Vocab Review Dividend Divisor 2)3()65( 2 +=+÷++ xxxx Quotient
• 6. 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
• 7. 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.”
• 8. Preparing for Synthetic Division, cont. xxx 273 35 −+ +−+++ xxx 273 35 020703 2345 +−+++ xxxxx
• 9. 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.
• 10. *Synthetic Division Steps  Example Problem: )2()11183( 24 −÷+−− xxxx
• 11. 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
• 12. Step 1 2 Write the constant value of the divisor (c) here.
• 13. Step 2 2 Write all the coefficients of the expanded dividend here. 3 0 -8 -11 1
• 14. Step 3 2 “Drop” the 1st coefficient underneath the line. 3 0 -8 -11 1 3
• 15. Step 4 2 Multiply “c” by the last value underneath the line. Write their product just underneath the next coefficient. 3 0 -8 -11 1 6 3
• 16. Step 5 2 Add together the numbers in that column and write their sum underneath the line. 3 0 -8 -11 1 6 3 6
• 17. Step 6 2 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
• 18. Step 7 2 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
• 19. Step 8 – Naming the Quotient 2 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
• 20. Step 8 – Naming the Quotient 3 6 4 -3 -5 The number in the box is the remainder. =−÷+−− )2()11183( 24 xxxx
• 21. Your Turn  On your Synthetic Division Notes packet, solve for the quotient of problems 11 – 14 using synthetic division 11. 12. 13. 14.
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