Explain Polynomial Expressions

Introduction:

The monomials in a polynomial are called the terms and the highest degree of the terms, the degree of the polynomial. The coefficient of the highest power of x in a polynomial is called the leading coefficient of the polynomial. In this article we shall discus about polynomial expression and degree of polynomial expression in detail.

Polynomial Expressions:

Consider the algebraic expression 6x³ – 8x² + 3.it has three terms, namely 6x^3, -8x² and 3

The power of x in the term 6x² is 3

The power of x in the term -8x² is 2

The third term 3 is a constant term or an independent term.

We note that in this expression the power of the value x are whole numbers.

Hence we call this algebraic expressions as polynomial expressions.

In the above expression the power of x is 3. The power should be a constant. it should be a variable. It must be an independent term. But we can write 3 as 3 * x⁰ ( since the value of x⁰ is 1).hence the power x in the term 3 is 0.

Note:

The power of any variable in the independent term is always 0.

Now consider another algebraic expression 2x³ – 3x^3/2 + 7x + 10.

It has 4 terms namely 2x³, -3x3^/2, 7x and 10.

In the second term -3x3^/2, the power of x is 3/2.the power is not a whole number. Therefore this algebraic expression cannot be called as a polynomial expression.

In an algebraic expression if the power of each variable is a whole number, it is called polynomial expression or simply a polynomial.