- An algebraic expression of the form 1 2 0 1 2 1 … n n n n n a x a x a x a x a − − + + + + − + , where 0 1 2 , , … n a a a a are real numbers, n is a non-negative integer and 0 a ≠ 0 is called a polynomial of degree n.
- Degree: The highest power of x in a polynomial p(x) is called the degree of polynomial.
- Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.
- Types of Polynomial:
**Constant Polynomial**: A polynomial of degree zero is called a constant polynomial and it is of the form p(x) = k.**Linear Polynomial:**A polynomial of degree one is called linear polynomial and it is of the form p(x) = ax + b where a, b are real numbers and 0 a ≠ 0.**Quadratic Polynomial:**A quadratic polynomial in x with real coefficient is of the form 2 ax bx c + + , where a, b, c are real numbers with a ≠ 0 .**Cubical Polynomial:**A polynomial of degree three is called cubical polynomial and is of the form p(x) = 3 2 ax + bx + cx + d where a, b, c, d are real numbers and a ≠ 0 .**Bi-quadratic Polynomial:**A polynomial of degree four is called bi-quadratic polynomial and it is of the form 2 3 2 p(x) = ax + bx + cx + dx + e , where a, b, c, d, e are real numbers and a ≠ 0 .

- The zeroes of a polynomial p(x) are precisely the x–coordinates of the points where the graph of y = p(x) intersects the x-axis i.e. x = a is a zero of polynomial p(x) if p(a) = 0.
- A polynomial can have at most the same number of zeros as the degree of polynomial.
- For quadratic polynomial 2ax + bx c + (a ≠ 0) Sum of zeros = ba − Produce of zeros = c a
- The division algorithm states that given any polynomial p(x) and polynomial g(x), there are polynomials q(x) and r(x) such that: p ( x g ) = ( x). q x r ( ) + ( x), g ( x ) ≠ 0 where r(x) = 0 or degree of r(x) < degree of g(x)
- The division algorithm states that given any polynomial p(x) and polynomial g(x), there are polynomials q(x) and r(x) such that: p(x) = g(x). q (x) + r(x), g(x) = 0 where r(x) = 0 or degree of r(x) < degree of g(x).

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