How to tackle 8th grade Polynomial Functions

In my opinion, Polynomial functions are one of the interesting areas of studies but sometimes it comes with so much complexities that it becomes quite a bit difficult to solve them. So the most necessary thing to understand is that we need to practice it a lot and it requires full concentration while solving it. Polynomial is basically a term which deals in almost every type of mathematical equations or statements. The most common terminologies used in polynomial expressions comes in eighth standard mathematics are monomial, binomial and trinomials. Algebraic equation with all variables having whole number, exponents or powers are called polynomials. The expressions in which the power of variables are negative and which include rational numbers are not polynomials. Algebraic expression having single term is known as Monomial and expression with two terms are known as Binomial whereas expressions with more than two terms or having three terms are known as Trinomials.

Now lets talk about Polynomial Functions. A polynomial functions p is basically a function or an expression that can be formed by combining the variable and some constants by a finite number of additions, subtractions, and multiplications.

A polynomial equation comes with the sum of the power of same derivatives and includes different integer constants, while the derivatives used are finite in numbers. The standard form of any polynomial equation is as:

b_n yⁿ + b_n-1 y^n-1 + ….......................+. b₂ y² + ….... + b₀ y⁰

Lets take some examples of Polynomial Equations to understand it better.

Function p (x) = x² – 3 is a polynomial of degree 2. in standard form it can be represented as : a₂ = 1, a₁= 0 and a₀ = -3.

An example to show a non polynomial function is P (d) = 1/d. This function becomes arbitrarily large for values of d close to zero and no polynomial does that.

Some examples of polynomial equations

A polynomial function f, is a function of the form f(x) = anxn + an-1xn-1 + ... + a2x2 + a1x1 + a0 where a0, a1...an are real numbers. It will soon become more understandable  with some more examples. If "n" is not zero, then f is said to have degree n. A polynomial f(x) with real coefficients and of degree n has n zeros (not necessarily all different). Some or all are real zeros and appear as x-intercepts when f(x) is graphed. To make it more simple lets start by explaining the word polynomial, it is the word which comes made of two terms "poly" states many and nominal states "terms". Nomenclature of different  polynomial functions, depending upon the terms present in the equation is done such as, if it has only one term it is called as monomial, if two terms it is called as binomial and if three terms it is called as trinomial, and so on with increasing variable terms.

Lets make it more elaborate with the help of examples, X + X>2 = 4  is an example of monomial, x + y = 5 is an example of binomial, X + Y + Z = 7 is an example of trinomial. When there are equations involving polynomial it is known as a Polynomial equation. For solution of a polynomial equation different values for variables in the equation satisfying the equation along with the given constant coefficient values used in the polynomial.

Lets see it practically with the help of some example, 5 x + 6 y = 0 is a polynomial equation, for a point A in a plane having coordinates (0, 0). Co-ordinates states value of x = 0, and y = 0 for this equation. Substituting values of x and y in the Polynomial equations  we have 5 (0) + 6 (0) = 0 + 0 = 0. As the values on both sides of the equation are equal this is a solution of the equation. Hence point A is the solution for this Polynomial equations.

TutorVista help on Polynomials

Polynomial is one of the most important term used in mathematical world which plays an important role in almost every type of mathematical equations or statements. Terminologies or concepts used in Polynomial equations are are monomial, binomial and trinomials. Algebraic equation with all variables having whole number, exponents or powers are called polynomials. Monomials are the Algebraic expression consist of single term and those algebraic expression comes equipped with two terms are known as Binomial Whereas the expressions with more than two terms or having three terms are known as Trinomials.


Lets talk about Polynomial functions used in mathematics. Polynomial function includes various things like terms, factors, variables, and constants. Let us talk about all the above terminologies in detail which are required to form a polynomial function. Terms can be explained as when numbers are implemented with addition or subtraction are known as terms. Terms can be further divided in to two sections that are Like terms or Unlike terms. Terms that has the same power of the same variables are called Like terms. The terms used in an expression that do not contain the same power of the same variables are called unlike terms. In an expression if the product of the numbers are used then the expression is called as factors. Variables are just representing a symbol which uses different values under it whereas constant is a single value symbol.


A polynomial equations comes with the sum of the power of same derivatives and includes different integer constants, while the derivatives used are finite in numbers.


Lets take some examples of Polynomial equations to understand it better.


7xyz : Monomial


x + 7y : Binomial


x + 3y – c : Trinomial


 

Learn Polynomial functions by taking help of Tutorvista

In mathematics, problems are represented in expression form on which standard principles of math are applicable. The major part of mathematical problems is represented in form of any polynomial function. A polynomial is a mathematical expression which may consist of various derivatives of various orders which are related with each other by arithmetical operators to form an math expression.

The standard form of any polynomial is as:

c_nyⁿ + c_n-1 y^n-1 + .......................+c₂ y² + ….... + c₀y⁰

The standard form consists of derivatives of only one variable, but as the name suggests “poly” means many ,  and “nomial” means terms, it means polynomial may consist of derivatives of different variables in it. According to this property polynomial equations are further categorizes as: monomial, binomial, trinomial and so on. Every polynomial function consist of different terms, factors, variables and constant integers coefficients. If two numbers or variables are combined through addition or subtraction operator then they form a term and if the degree of all those terms is same then they are said to be like terms otherwise unlike terms. The numbers are multiplied or product of two numbers is used in a polynomial than that part of it is known as factor. Variable is a symbol which represents the value which may change and constant is a fixed numerical value.

Let's see few examples of polynomial equations to explore more about it:

y – y² = 2 (a Monomial equation)

x + y = 2 (Binomial equation)

x + y - z = 1 (Trinomial equation)

All the algebraic equations like linear equations, quadratic equations, etc and they are different kind of polynomial equations also and for solving these polynomial equations the variables of the functions should be replaced by appropriate numerical value which will satisfy the equation in the end. To learn more about this topic switch to tutorvista.

Solving polynomial equations of mathematics

Polynomial is basically a term which deals in almost every type of mathematical equations or statements. The most common terminologies used in polynomial expressions are monomial, binomial and trinomials. Algebraic equation with all variables having whole number, exponents or powers is called polynomial. The expressions in which the power of variables are negative and rational numbers are not polynomials. Algebraic expression having single term known as monomial and expression with two terms are known as binomial whereas expressions with more than two terms or having three terms are known as trinomials.

Polynomial functions come equipped with terms, factors, variables, and constants. Let us explore about all these required objects to form a polynomial function. When numbers are implemented with addition or subtraction then they are said to be terms.Terms are of two types Like terms or Unlike terms. Terms that have the same power of the same variable are called like terms. The terms used in an expression that do not contain the same power of the same variables are called unlike terms. In an expression if the product of the numbers are used then the expression is called as factors. Variables are just representing a symbol which uses different values under it whereas constant is a single value symbol.

Polynomial equations, come with the sum of the power of same derivatives and includes different integer constants, while the derivatives used are finite in numbers. The standard form of any polynomial equation is as:

b_nyⁿ + b_n-1 yⁿ-1 + ….......................+. b₂ y² + ….... + b₀y⁰

In the above equation, y is the variable and b is the integer coefficient used.

Lets see some of the examples of polynomial equations to understand it better.

10xyz : Monomial

3x + 7y : Binomial

3x + 7y – c : Trinomial

How to Solve Polynomials

Polynomial is a term which implies with every kind of mathematical expression. Polynomial function consists of terms, factors, variables, and constants. Let us explore about all these required objects to form a polynomial function, When numbers are implemented with addition or subtraction than they are said to be terms, when product of the numbers are used than that form is called factors. Variables are just representing a symbol which uses different values under it whereas constant is a single value symbol.

A polynomial equation includes sum of the power of same derivatives with different integer coefficients and these all derivatives are finite in numbers. The standard form of any polynomial equation is as:

b_n yⁿ + b_n-1 y^n-1 + ….......................+. b₂ y² + ….... + b₀ y⁰

Here y is the variable with n types of derivatives, 'b' is an integer co-efficient and 'n' represents the finite number of derivatives in polynomial equation.

Sometimes any polynomial equation may consist of number of different derivatives or variables. So according to this property polynomial is categorized in various types which are binomial, monomial, trinomial and so on.

A polynomial is said to be a monomial when it only have one single variable derivatives and if equations consist of derivatives of two variables than that is a form of binomial equation. Similarly a trinomial will include derivatives of 3 different variables. Let us take some examples of polynomial equations:

x – x² = 2 (a Monomial)

x + y = 1 (Binomial)

x + y + z = 3 (Trinomial)

In mathematics most of the equations are in form of polynomial equation like every algebraic equation is a type of polynomial equation. So it is clear that polynomial functions are important in mathematics equation formation so for enhancing your knowledge in this topic and various other math topics you can take online math help on a math tutoring website “ TutorVista”.