More on the Remainder Theorem (4.3.2)

Question 1

• The remainder theorem: If a polynomial p (x) is divided by (x – c), then its remainder is p (c). Note in (x – c), the c is subtracting; as a result, any constant must change its sign before being substituted into the polynomial.

Answer 1

• The remainder theorem: If a polynomial p (x) is divided by (x – c), then its remainder is p (c). Note in (x – c), the c is subtracting; as a result, any constant must change its sign before being substituted into the polynomial.

Question 2

• This theorem and synthetic division allow the evaluation of some really big and complicated polynomials that might otherwise just baffle everybody.

Answer 2

• This theorem and synthetic division allow the evaluation of some really big and complicated polynomials that might otherwise just baffle everybody.

Question 3

• The remainder will always have less value than the dividing expression.

Answer 3

• The remainder will always have less value than the dividing expression.

Question 4

• The remainder will not have any x-terms, or you would be able to continue dividing.

Answer 4

• The remainder will not have any x-terms, or you would be able to continue dividing.