e.g. x2 − 5x + 8, 5x, 8x2, x + 3, etc.
-> In other words, A polynomial is an algebraic expression of the form
a0 + a1x + a2x2 + ............... + anxn-1 + anxn
where, a0, a1, a2, ......., an are real numbers such that an ≠ 0 and n is a
non-negative integer.
Note:- Let p(x) be a polynomial having an expression of
a0 + a1x + a2x2 + ............... + anxn-1 + anxn then
a0, a1x, a2x2, ..............., anxn-1, anxn are called terms of the polynomials.
e.g. 5x + 7
Here, 5x, 7 are terms of the polynomials.
Types of polynomials
* On the basis of terms:-
1) Monomial- A polynomial having only one term is called a monomial.
e.g. 5x, 8x2, etc.
2) Binomial- A polynomial having two terms is called a binomial.
e.g. 5x + 7, x + 3, x2 − 5x, etc.
3) Trinomial- A polynomial having two terms is called a binomial.
e.g. x2 + 5x + 7, x3 + 5x + 3, x4 − 5x2 + x, etc.
Note:- The highest power of the variable in a polynomial is called a degree of the polynomial.
* On the basis of degree:-
1) Linear Polynomial- A polynomial having degree 1 is called Linear Polynomial.
e.g. 3x - 1, 5x, 7x + 2, x/3, etc.
2) Quadratic Polynomial- A polynomial having degree 2 is called Quadratic Polynomial.
e.g. x2 + 5x + 7, x2, x2 + 7, etc.
3) Cubic Polynomial- A polynomial having degree 3 is called Cubic Polynomial.
e.g. x3 + 5x + 7, x3, x3 - x2 + 7, x3 + 3, etc.
4) Biquadratic Polynomial- A polynomial having degree 4 is called Biquadratic Polynomial.
e.g. x4 - 5x + 7, x4 - x3 - x2 + 7, x4 + 3, x4, etc.
Other Polynomials
* Zero Polynomial- A polynomial whose value is 0 is called Zero Polynomial.
Note:- The degree of zero polynomial is not defined.
* Constant Polynomial- A polynomial whose value is a constant is called Constant Polynomial.
e.g. 7, 3, -2,√5, etc.
Note:- The degree of the constant polynomial is always 1.
* When a number 'a' is put in place of x of polynomial P(x) then the value of the polynomial at x=a is called the value of a polynomial.
it is denoted by P(a).
* A number 'a' is said to be a zero of the polynomial P(x) if P(a)=0 i.e. the value of polynomial P(x) at x=a is 0.
Important points
1) General form of the Linear equation is ax + b.
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