# 15 Equations of Higher Degree

# LEARNING OUTCOMES

After completion of this chapter, the student should be able to:

Use the remainder theorem to evaluate polynomials and to find remainders

Use the factor theorem to identify factors and zeros of polynomials

Perform synthetic division

Use the fundamental theorem of algebra to determine the number of roots of an equation

Solve equations given at least one root

Determine the possible rational roots of an equation

Determine the maximum possible number of positive and negative roots by using Descartes’ rule of signs

Solve polynomial equations of degree three and higher

Solve application problems involving polynomial equations

The errors in the hand-compiled mathematical tables used by the British ...

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