<p> Synthetic Division Worksheet …. Reminder! Below are a few examples of how it is done. </p><p>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. </p><p>So, the answer would be 1x3 – 7x2 + 14x – 8 </p><p>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. </p><p>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. </p><p>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.. </p><p>2 6 4 12 60 180</p><p>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 </p><p>1. (x3 – 7x – 6) ÷ (x – 2)</p><p>2. (4x2 + 5x + 8) ÷ (x + 1) </p><p>3. (x3 – 14x + 8) ÷ (x + 4)</p><p>4. (x2 + 10) ÷ (x + 4) </p><p>5. (10x4 + 5x3 + 4x2 – 9) ÷ (x + 1)</p><p>6. (x3 + 8x2 – 3x + 16) ÷ (x + 5)</p><p>7. (2x4 – 6x3 + x2 – 3x – 3) ÷ (x – 3)</p><p>8. (x4 – 6x3 – 40x + 33) ÷ (x – 7) </p><p>9. (4x4 + 5x3 + 2x2 – 1) ÷ (x + 1) </p><p>10. (-10x5 + 3x – 7) ÷ (x – 1) </p>