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How To Figure Polynomials : 2

Introduction about how to figure polynomials:

 A polynomial  is a mathematical expression involving a sum of powers inone or more variables multiplied by coefficients. Each piece of the polynomial and each part that is being added is called as term. Polynomial terms have variables which are raised to whole-number exponents .These are nosquare roots of variables, no variables in the denominator and  no fractional powers of any fractions.  A polynomial figure in one variablewith constant coefficients  is generally represented bythe expression 

 anxn+…+a2x2+a1x+a0


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Figuring polynomial


anxn+…+a2x2+a1x+a0

       Here a0, a1, a2,….an are real numbers, here n is a positive integers are called a polynomialin x. This type of figure is called a polynomial. Polynomials contain more than one term. Polynomials are the sums of monomials.

A monomial has one term: 8a or -10b2 or 80.
A binomial has two terms: -3s2 2, or 9z – 2a2
A trinomial has 3 terms: -7y2 3x, or 10z – 2p2 y

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

 

 Polynomialsare generally written in decreasing order of terms. The largest term orthe term with the greatest exponent in the polynomial is commonly written first. The first term in a polynomial is called a leading term. When a term contains an exponent it says you the degree of the term.


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Examples


How to figure terms of polynomials:

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

Ex2:

9x5 - 2x 3x4 - 2

- This 4 term polynomial has a leading term to the 5th degree and a term to the fourth degree. It is called a 5th degree polynomial.

Ex3::

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

One thing you will do when figuring polynomials is combine like terms.

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