Synthetic Substitution Worksheet

Synthetic Division Worksheet …. Reminder! Below are a few examples of how it is done.

4 3 2 EX. 1 (1x – 4x – 7x + 34x – 24) ÷ (x + 3) You set it up like this… WhateverWhatever numbernumber endsends upup inin thisthis positionposition isis thethe remainder.remainder. WithWith thisthis case,case, xx ++ 33 divideddivided intointo thethe x + 3 = 0 polynomialpolynomial evenly.evenly. -3 -3 -3 1 -4 -7 34 -24 x = -3 -3 21 -42 24 OnceOnce youyou finishfinish youyou putput thethe variablevariable xx backback ontoonto thethe numbernumber startingstarting oneone degreedegree 0 lowerlower thatthat itit waswas before.before. 1 -7 14 -8 InIn thisthis casecase youyou startstart withwith xx33 4 becausebecause itit waswas xx4 beforebefore thethe syntheticsynthetic division.division.

So, the answer would be 1x3 – 7x2 + 14x – 8

AnytimeAnytime youyou areare missingmissing exponentsexponents youyou MUSTMUST addadd inin thethe missingmissing terms.terms. So,So, ifif thethe highesthighest exponentexponent isis xx55,, thenthen youyou shouldshould seesee 4 3 2 anan xx4,, xx3,, xx2,, x,x, andand aa constantconstant term.term.

EX. 2 (2x5 – 14x3 + 24x) ÷ (x – 3) So, let’s rewrite it with those in there. (2x5 + 0x4 – 14x3 + 0x2 + 24x + 0) ÷ (x – 3) Now we can do the work.

WithWhenWithWhen thethe youyou remainder,remainder, havehave aa remainder,remainder, youyou addadd itityouitityou onto ontoontoonto addadd the thethethe thethe answer answeransweranswer remainderremainder and andandand put put putput ontoonto it ititit 3 2 0 -14 0 24 0 overtheoverthe answeranswer whatwhat theythey andand were wereputput it it dividingdividing overover 6 18 12 36 180 by.whatby.what theythey werewere dividingdividing byby..

2 6 4 12 60 180

4 3 2 180 So, the answer would be 2x + 6x + 4x + 12x + 60 + (x - 3) Divide the following: 1-5 use synthetic; 6-10 use long

1. (x3 – 7x – 6) ÷ (x – 2)

2. (4x2 + 5x + 8) ÷ (x + 1)

3. (x3 – 14x + 8) ÷ (x + 4)

4. (x2 + 10) ÷ (x + 4)

5. (10x4 + 5x3 + 4x2 – 9) ÷ (x + 1)

6. (x3 + 8x2 – 3x + 16) ÷ (x + 5)

7. (2x4 – 6x3 + x2 – 3x – 3) ÷ (x – 3)

8. (x4 – 6x3 – 40x + 33) ÷ (x – 7)

9. (4x4 + 5x3 + 2x2 – 1) ÷ (x + 1)

10. (-10x5 + 3x – 7) ÷ (x – 1)