Verify the Division Algorithm I.E. Dividend = Divisor × Quotient + Remainder, in Each of the Following. Also, Write the Quotient and Remainder. Dividend Divisor 15y4 − 16y3 + 9y2 − 10 3 Y+6 3y − 2 - Mathematics

Sum

Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.

Dividend	Divisor
15y⁴ − 16y³ + 9y2 −\[\frac{10}{3}\] y+6	3y − 2

Quotient = \[5 y^3 - 2 y^2 + \frac{5}{3}y\]

Remainder = 6
Divisor = 3y - 2

Divisor x Quotient + Remainder = (3y - 2) (5y³- 2y²+

\[\frac{5}{3}y\]+ 6

\[15 y^4 - 6 y^3 + 5 y^2 - 10 y^3 + 4 y^2 - \frac{10}{3}y + 6\]

\[15 y^4 - 16 y^3 + 9 y^2 - \frac{10}{3}y + 6\]

= Dividend

Thus,
Divisor x Quotient + Remainder = Dividend
Hence verified.

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Chapter 8 Division of Algebraic Expressions
Exercise 8.4 | Q 21.5 | Page 12