Algebra-2

Let's use the Remainder Theorem to evaluate the given polynomials at the specified values of ( c ) and verify the provided remainders. The Remainder Theorem states that the remainder of a polynomial f(x) when divided by ( x - c ) is equal to f(c).

A.

Value of ( c ): c = 2

Using the Remainder Theorem:

We need to calculate f(2):

Calculating each term:

+ 1 = 1

Putting it all together:

f(2) = 32 - 8 + 16 + 1 = 41

Remainder:

The remainder is 41, which matches your statement.

B.

Value of ( c ): c = 1  

Using the Remainder Theorem:

We need to calculate f(1):

Calculating each term:

Click "Show Answer" to reveal the answer and analysis