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3y^5+6y^3+7y^2+8y+9 divided by 3y^3+1 |
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Answer» Answer: Divisor = 3y³ +1 Dividend = 3y^5 + 6y⁴ + 6y³ + 7y² + 8Y +9 TO FIND: Quotient and Remainder SOLUTION: \begin{gathered}\begin{array}{c|ccccccc}& {y}^{2} + 2y + 2\\\CLINE{2-7}3y {}^{3} + 1&3 {y}^{5} &+6 {y}^{4} &6 {y}^{3} & + 7 {y}^{2} &+ 8y& + 9\\ &3 {y}^{5} && &+y^2 \\ &-&&&-\\\cline{2-8} & & + 6 {y}^{4} & + 6 {y}^{3} & + 6 {y}^{2} & + 8y &+ 9\\&&6Y^4&& &+ 2y\\ && - &&& - \\\cline{2-8} &&&6 {y}^{3} & + 6 {y}^{2} & + 6y&& + 9 \\&&&6 {y}^{ 3} & &&&+ 2\\ &&&-&&&-\\\cline{2-8}&&&& 6 {y}^{2}&+ 6y& + 7 \\\end{array}\end{gathered} \cline2−73y 3 +1 \cline2−8 \cline2−8 \cline2−8
y 2 +2y+2 3y 5
3y 5
−
+6y 4
+6y 4
6y 4
−
6y 3
+6y 3
6y 3
6y 3
−
+7Y 2
+y 2
− +6y 2
+6y 2
6y 2
+8y +8y +2y − +6y +6y
+9 +9 − +7
+9 +2
Hence we found, Quotient = y² + 2y +2 Remainder = 6y² + 6y +7 |
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