Question

What is the remainder when the polynomial p(x)=x^200

Answer 1

Step-by-step explanation:

p(1)=1-2+1–2+1+1+1=1

Note :

(i) 2×2^199=2^(1+199)=2^200

(ii) 2×2^49=2^(1+49)≈2^50

p(2)=2^200–2*2^199+2^50–2*2^49+2²+2+1=4+2+1=7

Since the divisor is quadratic ,let the remainder r(x) be (ax+b)

p(x)=q(x)(x-1)(x-2)+ax+b

p(1)=a+b=1...(A)

p(2) =2a+b=7

(minus ↑)→a=6

(A)→6+b=1→b=5

∴ r(x)=6x-5