Q5 of 84 Page 43

Divide first polynomial by second polynomial and write the answer in the form ‘Dividend = Divisor × Quotient + Remainder’.

i. x3 – 64; x – 4


ii. 5x5 + 4x4 – 3x3 + 2x2 + 2; x2 – x

i. The division is as follows:



x3-64 = [(x2 + 4x + 16) × (x-4)] + 0


x3-64 = (x2 + 4x + 16) × (x-4)


ii. The division is as follows:



5x5 + 4x4 – 3x3 + 2x2 + 2 = [(5x3 + 9x2 + 6x + 8) × (x2-x)] + 8x +2


Quotient = 5x3 + 9x2 + 6x + 8


Remainder = 8x + 2


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3

Subtract the second polynomial from the first.

i.


ii. 2ab2 + 3a2b – 4ab; 3ab – 8ab2 +2a2b

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Multiply the given polynomials.

i. 2x; x2 – 2x


ii. x5 – 1; x3 + 2x3 + 2


iii. 2y + 1; y2 – 2y3 + 3y

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Write down the information in the form of algebraic expression and simplify.

There is a rectangular farm with length (2a2 + 3b2) meter and breadth (a2 + b2) meter. The farmer used a square shaped plot of the farm to build a house. The side of the plot was (a2 - b2) meter. What is the area of the remaining part of the farm?

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Divide each of the following polynomials by synthetic division method and also by linear division method. Write the quotient and the remainder.

(2m2 – 3m + 10) ÷ (m – 5)