Finding Polynomials Given Zeros, Degree, and One Point (4.6.1)

Question 1

• The factor theorem states that (x – c) is a factor of f (x) if f (c) = 0.

Answer 1

• The factor theorem states that (x – c) is a factor of f (x) if f (c) = 0.

Question 2

• A real zero of a polynomial is a point where the graph intersects the x-axis. Also, if you substitute that point into the polynomial, its value equals 0; i.e., f (x) = 0 for (x – c).

Answer 2

• A real zero of a polynomial is a point where the graph intersects the x-axis. Also, if you substitute that point into the polynomial, its value equals 0; i.e., f (x) = 0 for (x – c).

Question 3

• Given three zeroes and one point on the curve, the third degree polynomial function can be determined because only one function will have all four elements in common.

Answer 3

• Given three zeroes and one point on the curve, the third degree polynomial function can be determined because only one function will have all four elements in common.