This is the ppt of maths chapter 2 polynomials by Devansh Rana

1. MATHS HOLIDAY
ASSIGNMENT
NAME= DEVANSH RANA CLASS=9th

2. WHAT IS A POLYNOMIAL ?
Polynomial is an expression that consist of Variables , Terms ,Exponents and
Constants . For Example:-3x2-2x-10 is a polynomial.
A polynomial is a function of the form f(x) = anxn + an−1xn−1 + ... +
a2x2 + a1x + a0

3. What are the types of polynomials ?
 In General, There are 3 types of polynomials . They are Monomial,
Binomial,Trinomial.
 Monomial: It is an expression that has one term. Ex:- x,y,a,etc.
 Binomial: It is an expression that has two terms.Ex:- 2x+y,2x-x ,etc.
 Trinomial: It is an expression that has three terms.Ex:- x3-3x+10,etc.
 A Polynomial can have any number of terms but not infinite.

4. What is the degree of a polynomial ?
 A polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation.
The degree indicates the highest exponential power in the polynomial (ignoring the coefficients).
For example: 6x4 + 2x3+ 3 is a polynomial. Here 6x4, 2x3, 3 are the
terms where 6x4 is a leading term and 3 is a constant term. The
coefficients of the polynomial are 6 and 2.
The degree of the polynomial 6x4 + 2x3+ 3 is 4.
Let’s take another example: 3x8+ 4x3 + 9x + 1
The degree of the polynomial 3x8+ 4x3 + 9x + 1 is 8.

5. Types of Polynomials Based on its degree

6. How to find the zeros of the polynomial
 Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a
whole. A polynomial having value zero (0) is called zero polynomial. The degree of a
polynomial is the highest power of the variable x.

7. What is a factor theorem ?
 Factor theorem is commonly used for factoring a polynomial and finding the roots of the
polynomial. It is a special case of a polynomial remainder theorem.
 As discussed in the introduction, a polynomial f(x) has a factor (x-a), if and only if, f(a) = 0. It is
one of the methods to do the factorisation of a polynomial.

8. What is an remainder theorem ?
 Remainder Theorem is an approach of Euclidean division of polynomials. According to this
theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn’t essentially an element of the
polynomial; you will find a smaller polynomial along with a remainder. This remainder that has
been obtained is actually a value of P(x) at x = a, specifically P(a). So basically, x -a is the
divisor of P(x) if and only if P(a) = 0. It is applied to factorize polynomials of each degree in an
elegant manner.
 For example: if f(a) = a3-12a2-42 is divided by (a-3) then the quotient will be a2-9a-27 and the
remainder is -123.

9. Thank You