Divide 3y +6y4 +6y3 + 7y2 + 8y + 9 by 3y + 1 and show that
Dividend = Divisor x quotient + remainder.
Answers
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