Question

if xsq-3x+2 is divided by x-2 then the remainder is​

Answer 1

Answer:

lets solve the question by using remainder and factor theorem

x^100 = P(x)*(x-2)(x-1) + R(x) [# (x^2-3x+2) = (x-2)(x-1)]

P(x) = quotient after dividing

R(x) = remainder

in your case the divisor is a 2nd order polynomial i.e. x^2-3x+2, therefore the remainder takes the form ax+b, where a,b are numeric constants. Now the equation becomes:

x^100 = P(x)*(x-2)(x-1) + (ax+b)

lets put x=1 i.e.

1^100 = 0 + a+b

1 =a+b --------------------- (1)

and x=2

2^100 = 0 + 2a+b

2^100 = 2a + b --------------- (2)

solving equation (1) and (2)

a = 2^100 - 1 &

b = 2 - 2^100

Now as we know R(x) = ax + b is the required expression, hence the answer is

R(x) = (2^100-1)x + (2-2^100) <- answer