# NCERT Class 10 Mathematics Formula CBSE Board Sample Problems Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Polynomial Expressions

A polynomial expression S (x) in one variable x is an algebraic expression in x term as

Where are constant and real numbers and is not equal to zero

### Some Important Point to Note

 S. no Points 1 are called the coefficients for 2 n is called the degree of the polynomial 3 When all are zero, It Is called zero polynomial 4 A constant polynomial is the polynomial with zero degree. It is a constant value polynomial 5 A polynomial of one Item is called monomial, two Items binomial and three Items as trinomial 6 A polynomial of one degree is called linear polynomial, two degree as quadratic polynomial and degree three as cubic polynomial

### Important Concepts on Polynomial

 Concept Description Zero՚s or roots of the polynomial It is a solution to the polynomial equation S (x) = 0 i.e.. a number “a” is said to be a zero of a polynomial if S (a) = 0.If we draw the graph of S (x) = 0, the values where the curve cuts the X-axis are called Zeros of the polynomial Remainder Theorem՚s If p (x) is an polynomial of degree greater than or equal to 1 and p (x) is divided by the expression (x-a) , then the remainder will be p (a) Factor՚s Theorem՚s If x-a is a factor of polynomial p (x) then p (a) = 0 or if p (a) = 0, x-a is the factor the polynomial p (x)

### Geometric Meaning of the Zeroes of the Polynomial

let՚s us assume

y = p (x) where p (x) is the polynomial of any form.

Now we can plot the equation y = p (x) on the Cartesian plane by taking various values of x and y obtained by putting the values. The plot or graph obtained can be of any shapes

The zeroes of the polynomial are the points where the graph meet x-axis in the Cartesian plane. If the graph does not meet x-axis, then the polynomial does not have any zero՚s.

Let us take some useful polynomial and shapes obtained on the Cartesian plane

### Relation between Coefficient and Zeroes of the Polynomial

 S. no Type of Polynomial General form Zero՚s Relationship between Zero՚s and coefficients 1 Linear polynomial 1 2 Quadratic 2 3 Cubic 3 4

#### Formation of Polynomial when the Zeroes Are Given

 Types of polynomial Zero՚s Polynomial Formed Linear k = a (x-a) Quadratic and OrOr Sum of the zero՚s) x + product of the zero՚s Cubic and

### Division Algorithm for Polynomial

let՚s p (x) and q (x) are any two polynomial with , then we can find polynomial s (x) and r (x) such that

Where r (x) can be zero or degree of degree of g (x)

Dividend

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