Question

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

`(y^3 - 3y^2 + 5y - 1) ÷ (y - 1)`

Answer 1

Synthetic Division:

Dividend = `y^3 - 3y^2 + 5y - 1`

Divisor = y − 1

Opposite of −1 = 1

The coefficient form of the quotient is (1, −2, 3). 

∴ Quotient = y² − 2y + 3 and Remainder = 2 

Linear Method:

`y^3 - 3y^2 + 5y - 1`

`= y^2 (y - 1) + y^2 - 3y^2 + 5y - 1`

`= y^2 (y - 1) - 2y (y - 1) -2y +5y - 1`

`= y^2 (y - 1) - 2y (y - 1) + 3(y -1) + 3 - 1`

`= (y - 1) (y^2 - 2y + 3) + 2`