Table of contents

0. Review of Algebra(0)
1. Equations & Inequalities(0)
2. Graphs of Equations(0)
3. Functions(0)
4. Polynomial Functions(0)
5. Rational Functions(0)
6. Exponential & Logarithmic Functions(0)
7. Systems of Equations & Matrices(0)
8. Conic Sections(0)
9. Sequences, Series, & Induction(0)
10. Combinatorics & Probability(0)

4. Polynomial Functions

Zeros of Polynomial Functions

4. Polynomial Functions

Zeros of Polynomial Functions: Study with Video Lessons, Practice Problems & Examples

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28PRACTICE PROBLEM

For the given polynomial function, find the zeros and for each zero, state its multiplicity and comment if it crosses the x-axis or touches the x-axis and turns around.
f(x) = - 4(x + 1)(x - 3)³(x - 2)⁴

ANSWERS OPTIONS

x = - 1 (Multiplicity: 1) - crosses the x-axis; x = 3 (Multiplicity: 3) - touches the x-axis and turns around; x = 2 (Multiplicity: 4) - touches the x-axis and turns around

x = - 1 (Multiplicity: 1) - crosses the x-axis; x = 3 (Multiplicity: 3) - touches the x-axis and turns around; x = 2 (Multiplicity: 4) - crosses the x-axis

x = - 1 (Multiplicity: 1) - crosses the x-axis; x = 3 (Multiplicity: 3) - crosses the x-axis; x = 2 (Multiplicity: 4) - touches the x-axis and turns around

x = 1 (Multiplicity: 1) - crosses the x-axis; x = - 3 (Multiplicity: 3) - touches the x-axis and turns around; x = - 2 (Multiplicity: 4) - crosses the x-axis