Polynomial in Standard Form

Introduction to polynomial in standard form:

A polynomial is either zero, or can be written as the sum of one or more non-zero terms The number of terms is finite. These terms consist of a constant  which may be multiplied by a finite number of variable. Each variable may have an  that is a non-negative integer, i.e., a natural numbers The exponent on a variable in a term is called the degreeof that variable in that term, the degree of the term is the sum of the degrees of the variables in that term, and the degree of a polynomial is the largest degree of any one term. Since x = x1, the degree of a variable without a written exponent is one. The degree of a constant term is 0. The coefficient of a term may be any number from a specified set.

Basic Concepts of Polynomial in Standard Form:

Terms of standard polynomial:

Standard form of polynomial is axn+bxn+cxn+d.It contains four terms and three variables and one constant.

Mononomial.

A polynomial contains only one terms is called as mononomial.

Example for monomial standard:

2x,8,3y2

Binomial.

A polynomial contains two terms mean it caaled as binomial.

Example for binomial standard form:

2x+6,3y+1,2x2+34

Trinomial

A polynomial contains three term mean called as trinomial

Example for trinomial standard form:

6x+7+4y,3x2+4x+9

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Polynomial in Standard Form-example Problem:

Example polynomial standard problems:

Polynomial Addition

Example 1: Find the sum of 4x4 – 7x2 + 8x + 4 and 5x + 7x3 – 2x2 +4

Solution:

(4x4 – 7x2 + 8x + 4) + (7x3 – 2x2 + 5x +4) = 4x4 + 7x3 – 7x2 – 2x2 + 8x + 5x + 4 +4

= 4x4 + 7x3 – (-9)x2 + (5+8)x + 4+4

= 4x4 + 7x3 +9x2 + 13x + 8

Polynomial subtraction

Example 2: Subtract 8x3 – 9x2 – 3 from 7x3 + 5x2 – 5x – 9.

Solution: (8x3 - 9x2 – 3) – (7x3 -5x+5x2 – 9)

8x3 - 9x2 – 3 – 7x3 +5x-5x2 + 9

= x3 -14x2 +5x – 3+9

=x3 -14x2 +5x +6

Answer x3 -14x2 +5x +6