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# 06 - Let's Recap - Polynomials - Class 10 - Maths Class 10 Notes | EduRev

## Class 10 : 06 - Let's Recap - Polynomials - Class 10 - Maths Class 10 Notes | EduRev

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Polynomials

Polynomial: An algebraic expression of the form p(x) = a
0
+ a
1
x + a
2
x
2
+ --- + a
n
x
n

where a
n
?0 is called a polynomial in variable x of degree n. Where a
0
, a
1
, ----- a
n

are real numbers and each power of x is a non-negative integer.
Example:- 2x
2
– 5x + 1 is a polynomial of degree 2.
Note: vx + 3 is not a polynomial.

Degree of a Polynomial: The highest power of x in a polynomial p(x) is called the
degree of polynomial.

Different types of Polynomial:

 Constant Polynomial: A polynomial of degree zero is called a constant
polynomial and it is of the form of p(x) = k

 Linear Polynomial: A polynomial of degree 1 is called a linear polynomial
and it is of the form p(x) = ax + b, where a, b are real numbers and a
n
?0.
For example: 3x – 3 , 5x, etc.

 Quadratic Polynomial: A polynomial of degree 2 is called a Quadratic
Polynomial and it is of the form of p(x) = ax
2
+ bx + c , where a, b, c are real
numbers and a
n
?0.
For example: 2x
2
+x - 1

 Cubic Polynomial: A polynomial of degree 3 is called a Cubic Polynomial
and it is of the form of p(x) = ax
3
+ bx
2
+ cx + d , where a, b, c, d are real
numbers and a
n
?0.
For example: x
3
– 1

 Bi-quadratic Polynomial: A polynomial of degree 4 is called a Bi-
quadratic Polynomial and it is of the form of p(x) = ax
4
+ bx
3
+ cx
2
+ dx + e,
where a, b, c, d and e are real numbers and a
n
?0.

Value of a Polynomial: The value of a polynomial p(x) at x =  in the given
polynomial and is denoted by p(x).

Page 2

Polynomials

Polynomial: An algebraic expression of the form p(x) = a
0
+ a
1
x + a
2
x
2
+ --- + a
n
x
n

where a
n
?0 is called a polynomial in variable x of degree n. Where a
0
, a
1
, ----- a
n

are real numbers and each power of x is a non-negative integer.
Example:- 2x
2
– 5x + 1 is a polynomial of degree 2.
Note: vx + 3 is not a polynomial.

Degree of a Polynomial: The highest power of x in a polynomial p(x) is called the
degree of polynomial.

Different types of Polynomial:

 Constant Polynomial: A polynomial of degree zero is called a constant
polynomial and it is of the form of p(x) = k

 Linear Polynomial: A polynomial of degree 1 is called a linear polynomial
and it is of the form p(x) = ax + b, where a, b are real numbers and a
n
?0.
For example: 3x – 3 , 5x, etc.

 Quadratic Polynomial: A polynomial of degree 2 is called a Quadratic
Polynomial and it is of the form of p(x) = ax
2
+ bx + c , where a, b, c are real
numbers and a
n
?0.
For example: 2x
2
+x - 1

 Cubic Polynomial: A polynomial of degree 3 is called a Cubic Polynomial
and it is of the form of p(x) = ax
3
+ bx
2
+ cx + d , where a, b, c, d are real
numbers and a
n
?0.
For example: x
3
– 1

 Bi-quadratic Polynomial: A polynomial of degree 4 is called a Bi-
quadratic Polynomial and it is of the form of p(x) = ax
4
+ bx
3
+ cx
2
+ dx + e,
where a, b, c, d and e are real numbers and a
n
?0.

Value of a Polynomial: The value of a polynomial p(x) at x =  in the given
polynomial and is denoted by p(x).

Graph of Polynomial:

 Graph of a linear polynomial p(x) = ax + b is a straight line
 Graph of a quadratic polynomial p(x) = ax
2
+ bx + c is a parabola which
open upwards like ? if  a > 0
 Graph of a quadratic polynomial p(x) = ax
2
+ bx + c is a parabola which
open downwards like n if  a < 0
 In general, a polynomial p(x) of degree n crosses the x- axis, at most n
points.

Zeroes of a polynomial:

 ? is said to be zero of a polynomial p(x) if p(?)= 0. The zeros of polynomial
p(x) are actually the X- coordinates of the points where the graph of y = p(x)
intersects the X-axis.
 A polynomial of degree “n” can have at most n zeros. For example: A linear
polynomial has only one zero, a quadratic polynomial has two zeroes and a
Cubic polynomial has three zeroes.

Division Algorithm for Polynomials:

 If p(x) and g(x) are any two polynomials with g(x) ?0 then we can find
polynomials q(x) and r(x) such that
P(x) = g(x) x q(x) + r (x)
i.e. Dividend = Divisor x Quotient + Remainder
where, r(x) = 0 or degree of r (x) < degree of g(x). This result is known as
the division algorithm for polynomials.

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## Crash Course for Class 10 Maths by Let's tute

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