Matching Graphs to Polynomial Functions (4.7.1)

Question 1

• Rational root theorem: Given f (x) = an x n + an-1 x n-1 + … + a1 x + ao, if p/q is a root of f (x), then p is a factor of ao and q is a factor of an.

Answer 1

• Rational root theorem: Given f (x) = an x n + an-1 x n-1 + … + a1 x + ao, if p/q is a root of f (x), then p is a factor of ao and q is a factor of an.

Question 2

• The rational root theorem is very important in locating possible roots for complicated polynomials. It greatly limits the number of possible roots you have to check and makes finding all the roots actually possible.

Answer 2

• The rational root theorem is very important in locating possible roots for complicated polynomials. It greatly limits the number of possible roots you have to check and makes finding all the roots actually possible.

Question 3

• When graphing polynomials, every maximum and minimum point marks a boundary separating two regions. A curve will tend to have as many regions as its degree.

Answer 3

• When graphing polynomials, every maximum and minimum point marks a boundary separating two regions. A curve will tend to have as many regions as its degree.

Question 4

• Multiplicity: the number of times a specific value is a root for a polynomial.

Answer 4

• Multiplicity: the number of times a specific value is a root for a polynomial.