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