Question

(0)
1) Prepared a polynomial if divided it by x + 2, quotiend is x2-x+1 and remainder is 5.
And write its degree.​

Answer 1

Answer:

first of all let's multiply by x2- x + 1 by X + 2

because dividend=divisor×quotient +remainder

x2-x+1×x+2+5

x3-3x2-3x+2

and also its degree is 3

Answer 2

Answer:

3

Step-by-step explanation:

Solution :

Let f(x) = Q(x) (x - 1)(x - 2) + Ax + B, where Ax + B is the remainder when the polynomial f(x) is divided by (x - 1)(x - 2).

Then, f(1) = Q(1) (1 - 1)(1 - 2) + A(1) + B, or

f(1) = A + B = 5 (given)…#1.

f(2) = Q(2) (2 - 1)(2 - 2) + A(2) + B, or

f(2) = 2A + B = 7(given)…#2.

Solving #1 and #2, we have A = 2, and B = 3.

Pluging the values of A and B in Ax + B => 2x + 3, which is the required remainder.

Answer : The remainder is 2x + 3.