Evaluating Polynomial Functions

The prefix poly- signifies “many,” whereas “nomial” denotes “numbers” or “terms.” A polynomial is a collection of numbers or phrases.

Polynomials are algebraic expressions that are formed by adding, subtracting, multiplying, dividing, and exponentiating integers and variables. By adding or deleting terms, we may make a polynomial. Polynomials are extremely valuable in a variety of fields, including science, engineering, and business. Expressions, which we have been studying in this course, and polynomials have certain similarities. Polynomials are a type of mathematical expressions and equations.

Polynomial

Polynomials are algebraic expressions that are formed by adding, subtracting, multiplying, dividing, and exponentiating integers and variables. A polynomial can be made by adding or deleting terms. Polynomials are extremely valuable in a variety of fields, including science, engineering, and business. Expressions, which we have been studying in this course, and polynomials have certain similarities. Polynomials are a type of mathematical expressions and equations. A simple integer can be used as a polynomial term. To be termed a polynomial term, an expression must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.

Polynomial Function

Polynomial functions are sums of terms consisting of a numerical coefficient multiplied by the independent variable’s unique power. When a polynomial is written in descending order, the first term is also the one with the largest exponent, and is referred to as the “leading” term. The degree of the leading term in any polynomial indicates the degree of the entire polynomial. By adding, multiplying, and exponentiating to a non-negative integer power, a polynomial expression may be created from constants and symbols known as variables or indeterminates. Integers are commonly used as constants, but any expression that does not include indeterminates and represents mathematical objects that can be added and multiplied can also be used. If two polynomial expressions can be transformed from one to the other using the standard addition and multiplication qualities of commutativity, associativity, and distributivity, they are considered to define the same polynomial.

Polynomial Equation

 Polynomial equations are equations that have polynomial expressions on both sides. A polynomial’s usual form may always be expressed in the form. A polynomial is an algebraic statement having variables, constants, and operations like addition, subtraction, multiplication, and division, as well as only positive powers associated with the variables. An equation is a mathematical statement that has an ‘equal to’ symbol between two algebraic expressions with equal values.

Guide on Evaluating Polynomial Function

We take the value(s) you’ve been provided, plug them in for the proper variable(s), then simplify to determine the resulting value when “evaluating” a polynomial.

For example: Let us Evaluate the polynomial 10x³ + 4x² + 9x + 10 at x =2

So, we have the polynomial:

 P (x) = 10x³ + 4x² + 9x + 10,

P ( 2 ) = 10 (2)³ + 4 (2)² + 9 (2) + 10

P ( 2 ) = 10 (8) + 4 (4) + 9 (2) + 10

P ( 2 ) = 80 + 16 + 18 + 10

P ( 2 ) = 124

Thus, the given polynomial will give 124 as a result if we take x = 2.

Step to Evaluating Polynomial Function

• Write down the problem

• Arrange them in high to low degree

• Put the value of variable

• Solve the problem by using suitable formula, calculations

• Get the result

Point to remember

• A polynomial is a mathematical equation made up of variables, constants, and exponents that are mixed using operations like addition, subtraction, multiplication, and division

• A degree of the polynomial is a polynomial equation with one variable with the greatest exponent

• If the number of variables is one or more, the polynomial is called a univariate or multivariate. As a result, a polynomial’s variables can only have positive powers

• A polynomial term can be a simple integer. An expression must have no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions to be considered a polynomial term.

Conclusion  

We conclude that one of the most significant topics in mathematics is polynomials. As a result, it is critical that you master polynomials. Furthermore, polynomials are excellent tools for honing a specific thinking skill. Factoring polynomials, for example, teaches pupils how to dismantle anything.