Question

Divide the following polynomial by synthetic division method and also by linear division method. Write the quotient and the remainder.

${\displaystyle (y^3-216)÷(y-6)}$

Answer 1

Synthetic Division:

Dividend = ${\displaystyle y^3-216=y^3+0y^2+0y-216}$

Divisor = y − 6

Opposite of −6 = 6

The coefficient form of the quotient is (1, 6, 36). 
∴ Quotient = y² + 6y + 36 and Remainder = 0

Linear Method:

${\displaystyle y^3-216}$

${\displaystyle =y^2(y-6)+6y^2-216}$

${\displaystyle =y^2(y-6)+6y(y-6)+36y-216}$

${\displaystyle =y^2(y-6)+6y(y-6)+36(y-6)+216-216}$

${\displaystyle =y^2(y-6)+6y(y-6)+36(y-6)}$

${\displaystyle =(y-6)\times (y^2+6y+36)}$