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

i. x3 – 64; x – 4 

ii. 5x5 + 4x4 – 3x3 + 2x2 + 2; x2 – x

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i. x3 – 64; x3 + 0x2 + 0x - 64

∴ Quotient = x + 4x + 16, Remainder = 0 

Now, Dividend = Divisor x Quotient + Remainder 

∴ x3 – 64 = (x – 4)(x2 + 4x + 16) + 0 

ii. 5x5 + 4x4 – 3x3 + 2x2 + 2 = 5x5 + 4x4 – 3x3 + 2x + 0x + 2

∴ Quotient = 5x3 + 9x2 + 6x + 8, Remainder = 8x + 2 

Now, Dividend = Divisor x Quotient + Remainder 

∴ 5x5 + 4x4 – 3x3 + 2x2 + 2 = (x2 – x)(5x3 + 9x2 + 6x + 8) + (8x + 2)

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