Algebra-2

Let's verify the remainder for each polynomial using the Remainder Theorem, which states that if f(x) is a polynomial and ( c ) is a constant, the remainder of the division of f(x) by (x - c) is equal to f(c).

A.

Value of ( c ):c = 1

Calculate f(1):

= 1 - 5 + 3 + 2

= 1 - 5 = -4

= -4 + 3 = -1

= -1 + 2 = 1

Remainder:

The remainder is 1, which matches the statement.

B.

Value of ( c ): c = -3

Calculate f(-3):

Calculating each term:  

-7(-3) = 21

Putting it all together:

f(-3) = -972 + 243 + 21 + 1

Calculating step by step:

-972 + 243 = -729

-729 + 21 = -708

-708 + 1 = -707

Remainder:

The calculated remainder is -707, which does not match the statement of -134.

C.