Question

x³-64; x-4 Divide first polynomial by second polynomial and write the answer in the form ‘Dividend = Divisor ´ Quotient + Remainder’.

Answer 1

(x^3 - 64) / (x-4)

= (x^3 - 4^3) / (x-4)

= (x-4)(x^2 + 16 - 8x) / (x-4)

= x^2 - 8x + 16

____________________

=> (x^3 - 64) = (x-4)(x^2 - 8x +16) + 0

Answer 2

Given x³- 64 ÷ x - 4

x -4) x³ + 0 + 0 -64(x²+4x+16

***** x³ - 4x²

___________

********* 4x² + 0

******** 4x² - 16x

_____________

*****************16x - 64

***************** 16x- 64

_________________

Remainder ( 0 )

Dividend = x³ - 64

Divisor = ( x - 4 ) ,

Quotient = ( x² +4x+16 )

Remainder = 0

RHS=divisor×quotient+remainder

= (x-4)(x²+4x+16)+0

= x(x²+4x+16)-4(x²+4x+16)

= x³ + 4x² + 16x - 4x² - 16x - 64

= x³ - 64

= LHS

= Dividend

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