The document discusses polynomials, defining them as expressions with non-zero coefficients and categorizing them based on the number of terms (monomials, binomials, trinomials) and their degree (linear, quadratic, cubic). It explains the concept of zeroes of polynomials and how to find them, as well as the factor theorem which relates roots and factors of polynomials. Additionally, the document includes examples to illustrate each concept clearly.

1. B.J.P.S Samiti’s
M.V.HERWADKAR ENGLISH MEDIUM HIGH SCHOOL
CLASS: 9th CHAPTER 2: POLYNOMIALS
Program:
Semester:
Course: NAME OF THE COURSE
Staff Name: VINAYAK PATIL 1

2. POLYNOMIALS
•(1) Polynomial : The expression which contains one
or more terms with non-zero coefficient is called a
polynomial. A polynomial can have any number of
terms.
For Example: 10, a + b, 7x + y + 5, w + x + y + z,
etc. are some polynomials
• (2) Degree of polynomial: The highest power of the
variable in a polynomial is called as the degree of
the polynomial.
For Example: The degree of p(x) = x5 – x3 + 7 is 5.

3. Types of Polynomials based on terms
• 1. Monomials – Monomials are the algebraic expressions
with one term, hence the name “Mono”mial. In other
words, it is an expression that contains any count of like
terms. For example, 2x, 4t, 21x2y, 9pq etc.
• 2. Binomials – Binomials are the algebraic expressions
with two unlike terms, hence the name “Bi”nomial. For
example, 3x + 4x2 , 10pq + 13p2q
• 3. Trinomials – Trinomials are the algebraic expressions
with three unlike terms, hence the name “Tri”nomial. For
example- 3x + 5x2 – 6x3

4. Types of Polynomials based on
degree(powers)
• (1) Linear polynomial: A polynomial of degree one is called a linear
polynomial. In general a linear polynomial can be expressed in the
form ax + b where a≠0
For Example: 2x – 7, x + 5, etc. are some linear polynomial.
• (2) Quadratic polynomial: A polynomial having highest degree of two
is called a quadratic polynomial. The term ‘quadratic’ is derived from
word ‘quadrate’ which means square. In general, a quadratic
polynomial can be expressed in the form ax2 + b x + c, where a≠0 and
a, b, c are constants.
For Example: x2 – 9, a2 + a + 7, etc. are some quadratic polynomials.
• (3) Cubic Polynomial : A polynomial having highest degree of three is
called a cubic polynomial. In general, a cubic polynomial can be
expressed in the form ax3 + bx2 + cx + d, where a≠0 and a, b, c, d are
constants.
For Example: x3 – 9x +2, a3 + a2 + a + 7, etc. are some cubic
polynomial.

5. Zeroes of a Polynomial
• Zeroes of a Polynomial: The value of variable for which
the polynomial becomes zero is called as the zeroes of
the polynomial. In general, if k is a zero of p(x) = ax + b,
then p(k) = a k + b = 0, i.e., k = - b/a.
• Hence, the zero of the linear polynomial ax + b is –b/a =
• -(Constant term)/(coefficient of x)
•
For Example: Consider p(x) = x + 2. Find zeroes of this
polynomial.
If we put x = -2 in p(x), we get, p(-2) = -2 + 2 = 0.
Thus, -2 is a zero of the polynomial p(x).

6. •A real number ‘a’ is a zero of a polynomial
p(x) if p(a) = 0. In this case, a is also called
a root of the equation p(x) = 0.
•Every linear polynomial in one variable
has a unique zero, a non – zero constant
polynomial has no zero, and every real
number is a zero of the polynomial.

7. Factorisation of Polynomials
•Factor theorem: If p(x) is a
polynomial of degree n ≥ 1 and a is
any real number then i) x – a is a
factor of p(x), if p(a) = 0 and ii) p(a) =
0, if x – a is a factor of p(x)

8. Algebraic Identities