Question

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

Answer 1

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)