Question

Y3+y2+2y+3 divided by y+2

Answer 1

Division

Given: y3 + y2 + 2y + 3

To find: divide y3 + y2 + 2y + 3 by y + 2

Solution

Method 1. division method

y + 2 ) y3 + y2 + 2y + 3 ( y2 - y + 4

y3 + 2y2

- -

_____________

- y2 + 2y

- y2 - 2y

+ +

_____________

4y + 3

4y + 8

- -

_____________

- 5

• Dividend = y3 + y2 + 2y + 3
• Divisor = y + 2
• Quotient = y2 - y + 4
• Remainder = - 5

Method 2. Grouping

y3 + y2 + 2y + 3

= y3 + 2y2 - y2 - 2y + 4y + 8 - 5

= y2 (y + 2) - y (y + 2) + 4 (y + 2) - 5

= (y + 2) (y2 - y + 4) - 5

Using divison algorithm, we write

• Dividend = y3 + y2 + 2y + 3
• Divisor = y + 2
• Quotient = y2 - y + 4
• Remainder = - 5

Answer 2

Division  :

Given: y3 + y2 + 2y + 3

To find: divide y3 + y2 + 2y + 3 by y + 2

Solution  :

Method 1. division method

y + 2 ) y3 + y2 + 2y + 3 ( y2 - y + 4

y3 + 2y2

- -

_____________

- y2 + 2y

- y2 - 2y

+ +

_____________

4y + 3

4y + 8

- -

_____________

- 5

- Dividend = y3 + y2 + 2y + 3

- Divisor = y + 2

- Quotient = y2 - y + 4

- Remainder = - 5

Method 2. Grouping

y3 + y2 + 2y + 3

= y3 + 2y2 - y2 - 2y + 4y + 8 - 5

= y2 (y + 2) - y (y + 2) + 4 (y + 2) - 5

= (y + 2) (y2 - y + 4) - 5

Using divison algorithm, we write

- Dividend = y3 + y2 + 2y + 3

- Divisor = y + 2

- Quotient = y2 - y + 4

- Remainder = - 5