3. In mathematics, a polynomial is an expression of finite length
constructed from variables and constants, using only the operations
of addition, subtraction, multiplication, and non-negative, whole-
number exponents. Polynomials appear in a wide variety of areas of
mathematics and science. For example, they are used to form
polynomial equations, which encode a wide range of problems, from
elementary word problems to complicated problems in the sciences;
they are used to define polynomial functions, which appear in
settings ranging from basic chemistry and physics to economics and
social science; they are used in calculus and numerical analysis to
approximate other functions.
4. Let x be a variable n, be a positive
integer and as, a ,a ,….a be constants
1 2 n
(real nos.)
Then, f(x) = a xn+ a xn-1+….+a x+x
n n-1 1 o
a xn,a xn-1,….a x and a are known as
n n-1 1 o
the terms of the polynomial.
a ,a ,a ,….a and a are their
n n-1 n-2
coefficient
s.
1 o
For example:
• p(x) = 3x – 2 is a polynomial in variable x.
• q(x) = 3y2 – 2y + 4 is a polynomial in variable y.
• f(u) = 1/2u3 – 3u2 + 2u – 4 is a polynomial in variable u.
5. •A polynomial of degree 1 is called a Linear
Polynomial. Its general form is ax+b where a is not
equal to 0
•A polynomial of degree 2 is called a Quadratic
Polynomial. Its general form is ax3+bx2+cx, where a
is not equal to zero
•A polynomial of degree 3 is called a Cubic
Polynomial. Its general form is ax3+bx2+cx+d,
where a is not equal to zero.
•A polynomial of degree zero is called a Constant
Polynomial
6. LINEAR POLYNOMIAL
For example:
p(x) = 4x – 3, q(x) = 3y are linear
polynomials.
Any linear polynomial is in the form
ax + b, where a, b are real
nos. and a ≠ 0.
QUADRATIC POLYNOMIAL
For example:
f(x) = √3x2 – 4/3x + ½, q(w) = 2/3w2 + 4
are quadratic polynomials with real
coefficients.
7. CUBIC POLYNOMIAL
For example:
f(x) = 9/5x3 – 2x2 + 7/3x _1/5
is a cubic polynomial in variable x.
CONSTANT POLYNOMIAL
For example:
If(x) = 7, g(x) = -3/2, h(x) = 2
are constant polynomials.
8. VALUE OF POLYNOMIAL
If f(x) is a polynomial and y is
any real no. then real no.
obtained by replacing x by y in
f(x) is called the value of f(x)
at x = y and is denoted by f(x).
ZEROES OF POLYNOMIAL
A real no. x is a zero of the
polynomial f(x),is f(x) = 0
Finding a zero of the
polynomial means solving
polynomial equation f(x) = 0.
14. α + β = - coefficient of x
Coefficient of x2
= -
b
a
αβ = constant term
Coefficient of x2
= c
a
15. α + β + γ = -Coefficient of x2
Coefficient of x3
= -b
a
αβ + βγ + γα =
c
Coefficient of x =
Coefficient of x3 a
αβγ = - Constant term
Coefficient of x3
= d
a
17. •ON FINDING THE
QUOTIENT AND
REMAINDER USING
DIVISION ALGORITHM.
•If f(x) and g(x) are
any two polynomials
with g(x) ≠ 0,then we
can always find
polynomials q(x), and
r(x) such that :
•ON CHECKING WHETHER
A GIVEN POLYNOMIAL IS
A FACTOR OF THE OTHER
POLYNIMIAL BY APPLYING
THEDIVISION
ALGORITHM
F(x) = q(x) g(x) +
r(x),
•
ON FINDING THE
Where r(x) = 0 or
degree r(x) < degree
gD(IxV)ISION ALGORITHM
FOR POLYNOMIALS.
REMAINING ZEROES OF A
POLYNOMIAL WHEN SOME
OF ITS ZEROES ARE GIVEN.
•ON VERYFYING THE
