1. SYNTHETIC DIVISION SYNTHETIC DIVISION IS USED TO FIND THE QUOTIENT AND REMAINDER OF THE POLYNOMIAL. JAYASHREE AGASTI

2. RULES FOR SYNTHETIC DIVISION 1.WRITE THE POLYNOMIAL IN COEFFICIENT FORM.IF THE DEGREE OF THE POLYNOMIAL IS 3 THEN THERE ARE 4 COEFFICIENTS. IF ANY TERMS ARE MISSING THENWRITE THE COEFFICIENT AS ZERO. 1.WRITE THE POLYNOMIAL IN COEFFICIENT FORM.IF THE DEGREE OF THE POLYNOMIAL IS 3 THEN THERE ARE 4 COEFFICIENTS. IF ANY TERMS ARE MISSING THENWRITE THE COEFFICIENT AS ZERO. EX.2X 3 – 13 X 2 +17X+12 CAN BE WRITTEN IN COEFF. FORM AS EX.2X 3 – 13 X 2 +17X+12 CAN BE WRITTEN IN COEFF. FORM AS 2 - 13 + 17 +12 2 - 13 + 17 +12

3. 2.WRITE THE DIVISOR. IF X – 2 IS THE DIVISOR THEN WRITE X = 2 AS THE DIVISOR. 2.WRITE THE DIVISOR. IF X – 2 IS THE DIVISOR THEN WRITE X = 2 AS THE DIVISOR. EX. 2 2 - 13 +17 +12 EX. 2 2 - 13 +17 +12 ----------------------------------- ----------------------------------- 3. WRITE 2 AS IT IS, MULTIPLY 2 BY 2, WRITE THE PRODUCT BELOW – 13, DO ALGEBRAIC ADDITION OF – 13 AND 4 WRITE THE ADDITION BELOW IT. 3. WRITE 2 AS IT IS, MULTIPLY 2 BY 2, WRITE THE PRODUCT BELOW – 13, DO ALGEBRAIC ADDITION OF – 13 AND 4 WRITE THE ADDITION BELOW IT.

4. MULTIPLY 2 AND – 9, WRITE -18 BELOW +17,ADD +17 AND – 18, WRITE -1 BELOW IT AND CONTINUE TILL YOU GET THE LAST VALUE WHICH IS OUR REMAINDER. THE REMAINING COEFF. FORM THE QUOTIENT. MULTIPLY 2 AND – 9, WRITE -18 BELOW +17,ADD +17 AND – 18, WRITE -1 BELOW IT AND CONTINUE TILL YOU GET THE LAST VALUE WHICH IS OUR REMAINDER. THE REMAINING COEFF. FORM THE QUOTIENT. THE DEGREE OF THE QUOTIENT POLYNOMIALIS 1 LESS THAN THE NO. OF COEFF.

5. EX. 2 2 -13 + 17 +12 EX. 2 2 -13 + 17 +12 4 - 18 - 2 4 - 18 - 2 --------------------------------------------------- --------------------------------------------------- 2 - 9 - 1 +10 2 - 9 - 1 +10 + 10 IS OUR REMAINDER. + 10 IS OUR REMAINDER. THE QUOTIENT IS 2 X 2 – 9 X – 1. THE QUOTIENT IS 2 X 2 – 9 X – 1.

6. EX. FIND THE REMAINDER WHEN THE POLYNOMIAL 2 X 4 – 6 X 3 + 2 X 2 – X + 2 IS DIVIDED BY X + 2. EX. FIND THE REMAINDER WHEN THE POLYNOMIAL 2 X 4 – 6 X 3 + 2 X 2 – X + 2 IS DIVIDED BY X + 2. - 2 2 - 6 + 2 - 1 + 2 - 2 2 - 6 + 2 - 1 + 2 - 4 + 20 - 44 + 90 - 4 + 20 - 44 + 90 -------------------------------------------------- -------------------------------------------------- 2 - 10 + 22 - 45 + 92 2 - 10 + 22 - 45 + 92 HERE R = + 92 AND Q = 2 X 3 – 10 X 2 + 22 X – 45. HERE R = + 92 AND Q = 2 X 3 – 10 X 2 + 22 X – 45.

7. EX. DIVIDE X 5 – 1 BY X -1 AND WRITE Q AND R. EX. DIVIDE X 5 – 1 BY X -1 AND WRITE Q AND R. 1 1 0 0 0 0 -1 1 1 0 0 0 0 -1 1 1 1 1 1 1 1 1 1 1--------------------------------------------------- 1 1 1 1 1 0 1 1 1 1 1 0 HERE R = 0 AND Q = X 4 +X 3 +X 2 + X + 1.