# NCERT Class 10 Mathematics Formula CBSE Board Sample Problems Part 2

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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 Zeroâ€™s or roots of the polynomial It is a solution to the polynomial equation S(x) =0 i.e. a number â€śaâ€ť 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 Theoremâ€™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) Factorâ€™s Theoremâ€™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

Letâ€™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 zeroâ€™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 Zeroâ€™s Relationship between Zeroâ€™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 Zeroâ€™s Polynomial Formed Linear k=a (x-a) Quadratic and OrOrSum of the zeroâ€™s)x +product of the zeroâ€™s Cubic and

### Division Algorithm for Polynomial

Letâ€™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