Algebra-2

Let’s use the Remainder Theorem to verify the given polynomials at the specified values of ( c ) and check 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 = 1  

Using the Remainder Theorem:

Calculate f(1):

Calculating each term:

+ 2 = 2

Putting it all together:

f(1) = 5 - 3 + 1 + 2 = 5

Remainder:

The remainder is 5, not 13.

B.

Value of ( c ): c = 0

Using the Remainder Theorem:

Calculate f(0):

Calculating each term: