College Algebra 9th txtbk

SECTION R–3 Polynomials: Basic Operations and Factoring 21
95. PHYSICS—RELATIVISTIC MASS The mass M of an object
moving at a velocity v is given by
M M 0
A 1 v2
c 2
where M 0 mass at rest and c velocity of light. The mass of an
object increases with velocity and tends to infinity as the velocity
approaches the speed of light. Show that M can be written in the
form
M M 0c2c 2 v 2
c 2 v 2
96. PHYSICS—PENDULUM A simple pendulum is formed by hanging
a bob of mass M on a string of length L from a fixed support
(see the figure). The time it takes the bob to swing from right to left
and back again is called the period T and is given by
T 2 A
L
g
where g is the gravitational constant. Show that T can be written in
the form
T 21gL
g
R-3 Polynomials: Basic Operations and Factoring
Z Polynomials
Z Addition and Subtraction
Z Multiplication
Z Factoring
In this section, we review the basic operations on polynomials. Polynomials are expressions
such as x 4 5x 2 1 or 3xy 2x 5y 6 that are built from constants and variables
using only addition, subtraction, and multiplication (the power x 4 is the product
x x x x). Polynomials are used throughout mathematics to describe and approximate
mathematical relationships.
Z Polynomials
Algebraic expressions are formed by using constants and variables and the algebraic operations
of addition, subtraction, multiplication, division, raising to powers, and taking roots.
Some examples are
2 3 x 3 5 5x 4 2x 2 7
x 5
x 2 1 1
2x 5
1 1 x
An algebraic expression involving only the operations of addition, subtraction, multiplication,
and raising to natural number powers is called a polynomial. (Note that raising
to a natural number power is repeated multiplication.) Some examples are
2x 3 4x 2 3x 7
x 2y x 3 3x 2 y xy 2 2y 7