The Factor Theorem and Its Uses (4.4.1)

Question 1

• The factor theorem says (x – c) must be a factor of the polynomial if it divides into the polynomial with a remainder of 0. Also, if you substitute c into f (x), f (c) = 0.

Answer 1

• The factor theorem says (x – c) must be a factor of the polynomial if it divides into the polynomial with a remainder of 0. Also, if you substitute c into f (x), f (c) = 0.

Question 2

• The remainder theorem says that for (f(x))/x-c, the remainder is f (c).

Answer 2

• The remainder theorem says that for (f(x))/x-c, the remainder is f (c).

Question 3

• Synthetic division only works when the divisor is in the form, x - c. Also, remember before you divide to arrange the powers in the dividend in descending order and have a term for every power even if the term must have a coefficient of 0

Answer 3

• Synthetic division only works when the divisor is in the form, x - c. Also, remember before you divide to arrange the powers in the dividend in descending order and have a term for every power even if the term must have a coefficient of 0