Question

Describe the process of synthetic division . When is synthetic division not useful for dividing polynomials?
First, define the key terms; dividend, divisor and quotient. Then , outline the steps and give an example with details. Finally, talk about when synthetic division can and cannot be used?
What happens when we divide a polynomial by x? Can we use synthetic division to do this? What about when we divide a polynomial by x × x? What about x× n where n is a positive integer?
Can you use synthetic division repeatedly to divide by ( x- a)n ? How might you do this?

Answer 1

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Date: Page: divided. Dividend : The number being Divisor: A number that will divide the dividend exactly. Quotient : The result a division. tic Division Synthetic Example: 22²-5a²+ 32 +7 2-2 Stepti To set up the problem, first, get the denominator equal to 0. to find the number to put in the division box. Next, make sure the numerator is written in dexending oder and it any terms are visareng you must use a zero to fill in the Pressing term, finally dist only the coefficient in felie dollision problem. 21 2 - 5 3 7

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Page: Steps - Multiply the number in the diuisson box with the number brought down and but the result in the next column. 2) 3 -5 4 -2 7 f 2 Steps: Add the two numbers together of the row 2 and cwrite the result of the bottom 2 7 -5. 3 4 -2 2 Step 6. Multiply brought the number in the division box with the number you down & put the result & the next column 21 2 こち 3 4 -2 2 7 2 1 2020-7-31 14:36

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Step® Add the two numbers and write the result in the together bottom of the now 2 2 3 1 - 2 4 → 2 - row Step Woite the final anower. to The final answer is made up of the numbers in the bottom with the last number being the remainder and the remainder must be written as fractions The variables asn's start One power loss than the original denominator and go down on with each torm! 2:22-ati 2-2 Here as quotient remainder 2020-7-31 14:36

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Page Pose Synthetic division used when it mus be dividing by a and the leading coeffichent (first Synthetic divºrlm to dildo linear expressar For ex n+ 3 or a-6.etc. by ste Synthetic division cannot use to divide by 12+2 322 - 4 +7. of the leading coofficient is not a g. then it must divide by the to leading ceofficient to turn the leading coefficier 3n-1 would become 2-3 and 2n+ 7 would become at Z. polynomial by a we get the answer a power less than the given polynonnial of all! cofficient of the polynomial. but heres! for ex i When we divide a then we not use the synthetic method. 2020-7-31 14:36

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Date for exi 223 – 5x² + 3nt7 Applying eynthetie diuision, - 5 3 7 2 3 7 Answer - 2x² - 6x +3 +7 x je 22 When we dinde a polynomial by axa It tan divide by long method. Here we can't use Seynthetic diuion because g2 Pe not the linear expression es Whes we divide exnie na Here, we not use the synthetic diuision because it not leade leading coefficient be t. 2020-7-31 14:36

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Date: Page: We can n-a use synthetie ding repeatedly to dride by but if (a-an Then it would might be com become na - na na-na x- na n 2020-7-31 14:36