Intermediate[Math]-Polynomials

Polynomials
are algebraic expressions that include real numbers and variables.
Division and square roots cannot be involved in the variables. The
variables can only include addition, subtraction and multiplication.

Polynomials contain more than one term. Polynomials are the sums of monomials.

A monomial has one term: 5y or -8x² or 3.
A binomial has two terms: -3x² 2, or 9y - 2y²
A trinomial has 3 terms: -3x² 2 3x, or 9y - 2y² y

The degree of the term is the exponent of the variable: 3x² has a degree of 2.
When the variable does not have an exponent - always understand that there's a '1' e.g., 1^x

Example:

x² - 7x - 6

(Each part is a term and x² is referred to as the leading term.)

Term	Numerical Coefficient
x2 -7x -6	1 -7 -6

8x2 3x -2	Polynomial	3
8x-3 7y -2	NOT a Polynomial	The exponent is negative.
9x2 8x -2/3	NOT a Polynomial	Cannot have division.
7xy	Monomial	s

Polynomials
are usually written in decreasing order of terms. The largest term or
the term with the highest exponent in the polynomial is usually written
first. The first term in a polynomial is called a leading term. When a
term contains an exponent, it tells you the degree of the term.

Here's an example of a three term polynomial:

6x² - 4xy 2xy
- This three term polynomial has a leading term to the second degree.
It is called a second degree polynomial and often referred to as a
trinomial.

9x⁵ - 2x 3x⁴ - 2
- This 4 term polynomial has a leading term to the fifth degree and a
term to the fourth degree. It is called a fifth degree polynomial.

3x³ - This is a one term algebraic expression which is actually referred to as a monomial.

One
thing you will do when solving polynomials is combine like terms. This
is also discussed in lesson 2 - Adding and Subtracting polynomials.

Like terms: 6x 3x - 3x

NOT like terms: 6xy 2x - 4

The first two terms are like and they can be combined:

5x² 2x² - 3

Thus:

10x⁴ - 3

You are now ready to begin adding and subtraction polynomials.

جيد

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