POLYNOMIAL

A polynomial is an expression that contains constants and variables which is connected through basic operations of algebra. Variables are also known as indeterminates. The notation of a polynomial is p(x) where x represents the variable. For example: p(x)= .x²+3x-9.

We will discuss degree of polynomial , polynomial equation , polynomial function , types of polynomial. 

DEGREE OF A POLYNOMIAL

The degree of a polynomial is the greatest power of the variable in an expression.

For example: here the highest power is 4 so the degree of polynomial is 4.

There are three types of degree of polynomial:

A polynomial with degree 1 is called a linear polynomial.

For eg: 3x-1

A polynomial having degree 2 is known as a quadratic polynomial.

For eg:-3x²-2x+9

A polynomial with degree 3 is called a cubic polynomial.

For eg:-3×3+2×2+x+9

TYPES OF POLYNOMIALS

Three types of polynomials we have . They are classified on the basis of the number of terms in it.

Three types of polynomials:

• Monomial
• Binomial
• Trinomial

MONOMIAL: A polynomial which contains one non zero term is called a monomial.

For example: 2x^6 and many more

BINOMIAL: A polynomial having two non-zero terms is called a binomial.

For example: 2x+7 etc.

TRINOMIAL: A polynomial which contains three non-zero terms is called trinomial.

For example: 2×2-3x+x etc

PROPERTIES OF POLYNOMIAL

1.DIVISION ALGORITHM FOR POLYNOMIAL

If p(x) and g(x) are any two polynomials with g(x)  0, then we can  find the polynomials q(x) and r(x) such that 

                        P(x)=g(x)q(x)+r(x)

Where r(x)=0 or degree of r(x)<degree of g(x).

2.BEZOUT’S THEOREM

If p(a)=0 then polynomial p(x) is divisible by binomial (x-a). 

3.REMAINDER THEOREM 

If a polynomial f(x) is divided by x-k, then the remainder is the value f(k).

4.ZERO OR ROOT OF A POLYNOMIAL

The real number α Is a root or zero of a polynomial f(x), if f(α)=0.

POLYNOMIAL EQUATION

A polynomial equation is an equation that has various terms and generally includes variables coefficient and exponent. 

POLYNOMIAL FUNCTIONS

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc. 

CONCLUSION

 A polynomial is an expression that contains constants and variables which are connected through basic operations of algebra. Polynomials are unlike the other numbers students learn how to add, subtract, multiply and divide. We learn different types of polynomials, degree of polynomials and also  we use the division algorithm Theorem and the remainder theorem. We study types of polynomials which are Monomial , Binomial , Trinomial. Also we study properties of polynomials. And we will solve questions to make it more clear.

Also study polynomial equation which says that A polynomial equation is an equation that has various terms and generally includes variables coefficient and exponent and also talk about types of degree of polynomial