Question

Let f(x) = 2x ^ 2 + 7x + 1 Find the remainder when f(x) is divided by x-3,2x-3

Answer 1

Solution :

Case 1 :

f(x) = 2x² + 7x + 1

g(x) = x - 3

After Division of Polynomial we obtained

• Quotient = 2x + 13

• Remainder = 40

Verification :

★ Dividend = Divisor × Quotient + Remainder

→ 2x² + 7x + 1 = (x - 3) (2x + 13) + 40

→ 2x² + 7x + 1 = x(2x + 13) - 3 (2x + 13) + 40

→ 2x² + 7x + 1 = 2x² + 13x -6x - 39 + 40

→ 2x² + 7x + 1 = 2x² + 7x + 1

$\therefore$ Remainder obtained is 40.

Case 2 :

f(x) = 2x² + 7x + 1

g(x) = 2x - 3

After Division of Polynomial we obtained

• Quotient = x + 5

• Remainder = 16

Verification :

★ Dividend = Divisor × Quotient + Remainder

→ 2x² + 7x + 1 = (2x - 3) (x + 5) + 16

→ 2x² + 7x + 1 = 2x(x + 5) - 3(x + 5) + 16

→ 2x² + 7x + 1 = 2x² + 10x -3x -15 + 16

→ 2x² + 7x + 1 = 2x² + 7x + 1

$\therefore$ Remainder obtained is 16 .

Refer to the attachment!