Question

11 th question please help

Answer 1

Answer:

Option(D)

Step-by-step explanation:

Given: f(x) = x²⁰⁰ - 2x¹⁹⁹ + x⁵⁰ - 2x⁴⁹ + x² + x + 1

By Division algorithm, we get

⇒ x²⁰⁰ - 2x¹⁹⁹ + x⁵⁰ - 2x⁴⁹ + x² + x + 1 + Ax + B

Given that f(x) is divided by (x - 1)(x - 2).

(i) When x = 1:

1 - 2 + 1 - 2 + 1 + 1 + 1 + A + B

1 = A + B

(ii) When x = 2:

2²⁰⁰ - 2²⁰⁰ + 2⁵⁰ - 2⁵⁰ + 4 + 2 + 1

7 = 2A + B

On solving (i) & (ii), we get

A + B = 1

2A + B = 7

------------------

A = 6

Substitute A = 6 in (i), we get

⇒ A + B = 1

⇒ 6 + B = 1

⇒ B = -5

∴ Remainder = 6x - 5

Hope it helps!

Answer 2

P(x) / a quadratic ----> remainder = ax + b , with a , b constant  

remainder theorem ---> P(1) = .... = 1 = a+b  

and P(2) = ... = 7 = 2a + b  

solve 2 equations for a , b