Question

X square minus 1 divided by x to the power 45 find the remainder

Answer 1

Step-by-step explanation:

The remainder must be a polynomial of degree no greater than one.

remainder = r(x) = Ax + B

q(x)(x² - 1) + r(x) = x^45 (for some polynomial function q(x))

Let x = -1.

q(-1)[(-1)² - 1] + r(-1) = (-1)^45

0 + r(-1) = -1

-A + B = -1

Let x = 1.

q(1)[(1)² - 1] + r(1) = (1)^45

0 + r(1) = 1

A + B = 1

Now you have this system in A and B:

-A + B = -1

A + B = 1

A = 1, B = 0

(1)x + (0) = x

The remainder is x.

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