Class 10th
Mathematics
Short Note
\
Chapter 1- POLYNOMIALS
■ Polynomials:
A polynomial is an expression consisting of constants, variables
and exponents. Its mathematical form is-
f (x) = anxn + an−1xn−1 + …+a1x + a0, an 0 is called a
polynomial in variable x.
where x: variable
a: Real number
n: whole number
For example: P(x) = 3x −2 is a polynomial in variable x.
■ Degree of a Polynomial:
The highest power of x in a polynomial f(x) is called the degree
of the polynomial f f( x)
➢ Following are forms of various degree polynomials:
Degree Name of the polynomial Form of the polynomial
0 Constant polynomial f(x) = a, a is a constant
1 Linear polynomial f(x) = ax + b, a 0
2 Quadratic polynomial f(x) = ax2 + bx + c, a 0
3 Cubic polynomial f(x) = ax3 + bx2 + cx + d, a 0
4 Biquadratic polynomial f(x) = ax4 + bx3 + cx2 + dx + e, a
0
■ Value of Polynomial: Let p(y) is a polynomial in y and α
could be any real n number, then the value calculated
after putting the value y = α in p(y) is the final final value of p(y)
at y = α. This shows that p(y) at y = α is represented by p(α).
, ■ Zero of a Polynomial: If the value of p(y) at y = k is 0,
that is p(k) = 0 then y y = k will be the zero of that polynomial
p(y).
■ Geometrical meaning of the Zeroes of a
Polynomial: Zeroes of the p polynomials are the x
coordinates of the points where the graph of that polynompolynomial
intersects the x-axis.
■ Graph of a Linear Polynomial:
Graph of a linear polynomial is a straight line which intersects
the x-axis at one po int only, so a linear polynomial has degree 1.
■ Graph of Quadratic Polynomial:
➢ Case 1: When the graph cuts the x-axis at the two points then
these two points a are the two zeroes of that quadratic
Mathematics
Short Note
\
Chapter 1- POLYNOMIALS
■ Polynomials:
A polynomial is an expression consisting of constants, variables
and exponents. Its mathematical form is-
f (x) = anxn + an−1xn−1 + …+a1x + a0, an 0 is called a
polynomial in variable x.
where x: variable
a: Real number
n: whole number
For example: P(x) = 3x −2 is a polynomial in variable x.
■ Degree of a Polynomial:
The highest power of x in a polynomial f(x) is called the degree
of the polynomial f f( x)
➢ Following are forms of various degree polynomials:
Degree Name of the polynomial Form of the polynomial
0 Constant polynomial f(x) = a, a is a constant
1 Linear polynomial f(x) = ax + b, a 0
2 Quadratic polynomial f(x) = ax2 + bx + c, a 0
3 Cubic polynomial f(x) = ax3 + bx2 + cx + d, a 0
4 Biquadratic polynomial f(x) = ax4 + bx3 + cx2 + dx + e, a
0
■ Value of Polynomial: Let p(y) is a polynomial in y and α
could be any real n number, then the value calculated
after putting the value y = α in p(y) is the final final value of p(y)
at y = α. This shows that p(y) at y = α is represented by p(α).
, ■ Zero of a Polynomial: If the value of p(y) at y = k is 0,
that is p(k) = 0 then y y = k will be the zero of that polynomial
p(y).
■ Geometrical meaning of the Zeroes of a
Polynomial: Zeroes of the p polynomials are the x
coordinates of the points where the graph of that polynompolynomial
intersects the x-axis.
■ Graph of a Linear Polynomial:
Graph of a linear polynomial is a straight line which intersects
the x-axis at one po int only, so a linear polynomial has degree 1.
■ Graph of Quadratic Polynomial:
➢ Case 1: When the graph cuts the x-axis at the two points then
these two points a are the two zeroes of that quadratic
