Question

Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:

5y³ − 6y² + 6y − 1, 5y − 1

Answer 1

$$\frac{5y^3-6y^2+6y-1}{5y-1}$$
$$=\frac{y^2(5y-1)-y(5y-1)+1(5y-1)}{(5y-1)}$$
$$=\frac{(5y-1)(y^2-y+1)}{(5y-1)}$$
$$=(y^2-y+1)$$
$$\text{Therefore,}$$
$$\text{Quotient = y^2 - y + 1 and remainder = 0}$$