# Polynomials CBSE Class 10 Maths Revision Notes Chapter 2

A polynomial is an expression consists of constants, variables and exponents. It’s mathematical form is-

a­­­nxn + an-1xn-1 + an-2xn-2 + a2x2 + a1x + a0 = 0

where the (ai)’s are constant

## Degree of Polynomials

Let P(y) is a polynomial in y, then the highest #ffffcc power of y in the P(y) will be the degree of polynomial P(y).

## Types of Polynomial according to their Degrees

 Type of polynomial Degree Form Constant 0 P(x) = a Linear 1 P(x) = ax + b Quadratic 2 P(x) = ax2 + ax + b Cubic 3 P(x) = ax3 + ax2 + ax + b Bi-quadratic 4 P(x) = ax4 + ax3 + ax2 + ax + b

## Value of Polynomial

Let p(y) is a polynomial in y and α could be any real number, then the value calculated after putting the value y = α in p(y) is the final value of p(y) at y = α. This shows that p(y) at y = α is represented by p (α).

## Zero of a Polynomial

If the value of p(y) at y = k is 0, that is p (k) = 0 then y = k will be the zero of that polynomial p(y).

### Geometrical meaning of the Zeroes of a Polynomial

Zeroes of the polynomials are the x coordinates of the point where the graph of that polynomial intersects the x-axis.

## Graph of a Linear Polynomial

Graph of a linear polynomial is a straight line which intersects the x-axis at one point only, so a linear polynomial has 1 degree.

Case 1: When the graph cuts the x-axis at the two points than these two points are the two zeroes of that quadratic polynomial.

Case 2: When the graph cuts the x-axis at only one point then that particular point is the zero of that quadratic polynomial and the equation is in the form of a perfect square

Case 3: When the graph does  not intersect the x-axis at any point i.e. the graph is either completely above the x-axis or below the x-axis then that quadratic polynomial has no zero as it is not intersecting the x-axis at any point.

Hence the quadratic polynomial can have either two zeroes, one zero or no zero. Or you can say that it can have maximum two zero only.

## Division Algorithm for Polynomial

If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find 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).

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