# 4 definition by hotgirl69xxx

Top Definition
An expression such as
x^3 + 2x^2 - 6x - 2, is a cubic expression.
3x - 4 is linear
x^2 + 5x - 10 is quadratic

These types of expressions can be extended to include higher powers of x, such as
x^5 + 3x^3 - 2x^2 + 3
4x^6 + 2x^4 - x^3 + 5

Expressions of this type are called polynomials.
Note: Polynomials do not have negative or fractional powers. n is a non-negative integer.

The degree of a polynomial is given by the highest power of the variable
An expression of the form
ax^n + bx^(n-1) + ... + px^2 + qx + r
(where a, b, ..., p, q, r are constants is called a polynomial in x)

3x^5 + 3x^4 - 2x^2 -1 is a polynomial of degree 5.

A constant expression is a polynomial of degree 0
A linear expression is a polynomial of degree 1
a quadratic expression is a polynomial of degree 2
a cubic expression is a polynomial of degree 3
etc.
by December 27, 2004 In mathematics, we often arrive at answers that contain root signs (they may be square roots, cube roots, etc.).

We will find that some of these numbers with a root sign are easy to deal with since they have an exact decimal representation

For instance sqrt16 = 4, rt^3(8)= = 2, sqrt11.56 = 3.4, rt^5(1/32) = 0.5.

This is because each of these numbers is rational
Expressions with root signs involving pirrational numbers] such as sqrt7 - 2 or rt^3(5) are called surds.
by December 28, 2004 The plural of index is indices
Index is simply another word for power.
a * a * a * a can be written as a^4 (a to the power of 4)
by December 28, 2004 the reverse process of differentiaton

we know that, for example if f(x) = 2x^3 - 5x^2 + 3x -7
then f'(x) = 6x^2 - 10x + 3

This process can be reversed.

In general, y = x^n -> dy/dx = nx^(n-1)
So, reversing this process, it would seem that dy/dx = x^m -> y = (1/(m+1))x^(m+1)

The general process of finding a function from its derivative is known as interation.
Given that dy/dx = 12x^2 + 4x - 5, find an expression for y.

y = 12((x^3)/3) + 4((x^2)/2) - 5((x^1)/1)

It would seem that
y=4x^3 + 2x^2 - 5x

but that is not quite the complete answer

Whenever you differentiate a constant you get zero,
e.g. y = 7 dy/dx = 0
and so the expression for y above could have any constant on the end and still satisfy dy/dx = 12x^2 + 4x - 5
The answer to this example is therefore
y= 4x^3 + 2x^2 - 5x + c, where c is a constant.
by December 22, 2004 