Finding the Zeros of a Polynomial from Start to Finish (4.6.5)

Question 1

• The factor theorem says that (x – c) is a factor when f (c) = 0.

Answer 1

• The factor theorem says that (x – c) is a factor when f (c) = 0.

Question 2

• Finding all the zeros of a polynomial involves:

1. Listing all the possible real number candidates.
2. Testing the candidates to see which ones work.
3. Using division to factor out the (x - c) when you find a zero, or root.

Answer 2

• Finding all the zeros of a polynomial involves:

1. Listing all the possible real number candidates.
2. Testing the candidates to see which ones work.
3. Using division to factor out the (x - c) when you find a zero, or root.

Question 3

• Every rational integral function of n degree has exactly n roots.
• Some may be repeated.
• Some may be complex numbers, which always come in conjugate pairs.

Answer 3

• Every rational integral function of n degree has exactly n roots.
• Some may be repeated.
• Some may be complex numbers, which always come in conjugate pairs.

Question 4

• The rational root theorem says that every possible real number root is in the form of p/q:
• p is a factor of the constant at the end of the function, and
• q is a factor of the coefficient of the highest power.

Answer 4

• The rational root theorem says that every possible real number root is in the form of p/q:
• p is a factor of the constant at the end of the function, and
• q is a factor of the coefficient of the highest power.