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POLYNOMIAL
Have you ever wondered how computer graphics
software is able to so quickly draw the smooth,
life-like faces that we see in video games and
animated movies? Or how in architectural projects
builders compensate for the fact that a horizontal
beam, fixed in position at both ends, will bend
under its own weight? Can you imagine how
computers mould automotive body panels Believe it or not, all three tasks are possible
thanks to polynomials! Polynomials are composed
by applying addition, subtraction, and
multiplication to numbers and variables. The
information needed to perform certain tasks like
the ones listed above is reduced to the
polynomial segments between key points. Much
like words in language, polynomials are the
vocabulary of algebra, and, as such, they are used
in a wide variety of applications by designers,
engineers, and others. Calculus, the study of
motion and rates of change, requires a clear
understanding of polynomials, so we’ll begin our
study there.
CHAPTER EXPECTATIONS In this chapter, you will
determine properties of the graphs of polynomial functions, Section 1.1
sketch the graph of a polynomial function, Section 1.1
describe the nature of change in polynomial functions, Section 1.2
determine an equation to represent a given graph of a polynomial function, Career Link
understand the Remainder and Factor Theorems, Section 1.3, 1.4 Review of Prerequisite Skills Before beginning your study of Polynomial Functions, you may wish to review the following factoring methods that you learned in previous courses. Common Factor ? 4x2
2 Grouping ? By grouping terms together it is often possible to factor the grouped terms. Factor fully
y Trinomial Factoring ? Factor fully 3x2
4. Solution 1
by decomposition Solution 2
by inspection 3x2
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