Algebra-2

Let's verify the given examples using the Remainder Theorem for the polynomials you provided. The Remainder Theorem states that if you evaluate a polynomial f(x) at a value c, the result f(c) is the remainder when f(x) is divided by x - c.

A.

Value of c : c = -2

Using the Remainder Theorem:

We find f(-2):

Calculating each term:

-1

Putting it all together:

f(-2) = 256 - 24 - 1 = 231

Remainder:

The remainder is 231, not 41.

B.

Value of c : c = 2

Using the Remainder Theorem:

We find f(2):

Calculating each term:

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