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=Concept of Polynomial

 

Degree of the polynomial
Type of polynomials
Linear polynomial
Quadratic polynomial
Cubic polynomial
Zeros of the polynomial
Division Algorithm

Degree of the polynomial :- 

If p(x) is a polynomial in terms of  x, the highest power of x in p(x) is called the degree of the polynomial p(x).
For example:
3x + 2 is a polynomial of  x.  Degree of expression is 1
4z^2 –z + 2 is a polynomial of z.  Degree of expression is 2,
3x^3 – 2x – 2 is a polynomial of x.  Degree of expression is 3

Type of polynomials

 

Linear polynomial :-

A polynomial of degree 1 is called a linear polynomial.          

For example: 7x + 43

Quadratic polynomial :-

 A polynomial of degree 2 is called a quadratic polynomial.

For example:  x^2 + 3x + 7

 

Cubic polynomial :-

A polynomial of degree 3 is called a cubic polynomial

For example:  x^3 + 3x

 

Zeros of the polynomial :-

A real number t  is called a zero of a polynomial if the value of f(t) = 0
For example  
f(x)  = x^2 – 6x +8
zeros of this equation are 2 and 4 because
f(2)= 2^2 -6*2 + 8 = 0
f(4)= 4^2 – 6*4 + 8 =0

Sum and product of root of quadratic equation   :-
For a equation ax^2 + bx  + c  = 0 , if  root are α and β ,

sum or root and product of root.PNG

Roots for cubic equation :-
For a equation ax^3 + bx^2 + cx + d  = 0

cubic roots.PNG

Division Algorithm:-

If p(x) and g(x) are any two polynomials with g(x) is not equal to 0, then we can find polynomials q(x) and r(x) such that
If r(x) = 0 or degree of r(x) < degree of g(x).
Dividend         = Divisor × Quotient   + Remainder
p(x)      = g(x)     × q(x)          + r(x),



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Degree of the polynomial Type of polynomials Linear polynomial Quadratic p

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