NCERT Class 9 Maths Formula CBSE Board Sample Problems Part 2 (For CBSE, ICSE, IAS, NET, NRA 2023)

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2. 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

Some Important Point to Note
S. noPoints
1 are called the coefficients for
2n Is called the degree of the polynomial
3When all are zero, It Is called zero polynomial
4A constant polynomial Is the polynomial with zero degree It Is a constant value polynomial
5A polynomial of one Item Is called monomial, two Items binomial and three Items as trinomial
6A polynomial of one degree Is called linear polynomial, two degree as quadratic polynomial and degree three as cubic polynomial

Important Concepts on Polynomial

Important Concepts on Polynomial
Zero՚s or roots of the polynomialIt 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՚sIf 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՚sIf 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)