Remainder Theorem

[flakine]

Is there a trick that I'm missing? How can you solve with such large exponents. Synthetic division will take forever.

What is the remainder when:

X^500 +6X^201-X^2-2X+4

is divided by

X-1

 

[tkhunny]

X^500 +6X^201-X^2-2X+4

is divided by

X-1

If f(X) = X^500 +6X^201-X^2-2X+4, the remainder when divided by x-1 is f(1). Synthetic division is only evaluating the polynomial at the given value. It provides the intermediate values that also offer some advantages. Look up "Horner's Method."

 

[soroban]

Hello, flakine!

Is there a trick that I'm missing? How can you solve with such large exponents.
Synthetic division will take forever.

What is the remainder when:
. . X⁵⁰⁰ + 6X²⁰¹ - X² - 2X + 4 is divided by: X - 1
.

You mentioned the Remainder Theorem in your subject line.
. . but you're not acquainted with it?

As tkhunny pointed out: when f(x) is divided by x - a, the remainder is f(a).

So you need to evaluate: .f(1) .= .1⁵⁰⁰ + 6·1²⁰¹ - 1² - 2·1 + 4 . . . and tht's it!