# NCERT Solutions for Class 9 Maths Chapter 2

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials in Hindi & English Medium, PDF form as well as online digital contents updated for new academic session 2020-21 following the new CBSE Curriculum.

Download NCERT Solutions Apps 2020-2021 and Offline Solutions based on latest CBSE Syllabus for 2020-21.## NCERT Solutions for Class 9 Maths Chapter 2

Class: | 9 |

Subject: | Maths – गणित |

Chapter 2: | Polynomials |

### 9th Maths Chapter 2 Sols in English & Hindi Medium

### Class 9th Maths Chapter 2 Polynomials Solutions

- NCERT Solutions
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### Study Materials on 9th Maths Chapter 2

#### Important Terms on 9th Maths Chapter 2

1. A combination of constants and variables, connected by four fundamental arithmetical operations +, -, x and / is called an algebraic expression. e.g. 6x² – 5y² + 2xy

2. An algebraic expression which have only whole numbers as the exponent of one variable, is called polynomial in one variable. e.g. 3x³ + 2x² – 7x + 5 etc.

3. The part of a polynomial separated from each other by + or – sign is called a term and each term of a polynomial has a coefficient.

4. Highest power of the variable in a polynomial, is known as degree of that polynomial.

5. The value obtained on putting a particular value of the variable in polynomial is called value of the polynomial at the value of variable.

6. Zero of a polynomial p(x) is a number alpha, such that p(alpha) = 0. It is also called root pf polynomial equation p(x) = 0.

7. Let f(x) be any polynomial of degree n,(n ≥ 1) and a be any real number. If f(x) is divided by the linear polynomial (x-a), then the remainder is f(a).

8. Let f(x) be a polynomial of degree n,(n ≥ 1) and a be any real number. Then,

i). If f(a) = 0, then (x – a) is a factor of f(x).

ii). If (x – a) is a factor of f(x), then f(a) = 0.

##### Polynomial on the Basis of Number of Terms

1. A polynomial containing one non-zero term, is called a monomial.

2. A polynomial containing two non-zero terms, is called a binomial.

3. A polynomial containing three non-zero terms, is called a trinomial.

###### Polynomial on the Basis of Degree of Variables

1. A polynomial of degree 0, is called a constant polynomial.

2. A polynomial of degree 1, is called a linear polynomial.

3. A polynomial of degree 2, is called a quadratic polynomial.

4. A polynomial of degree 3, is called a cubic polynomial.

5. A polynomial of degree 4, is called a biquadratic polynomial.

### Important Questions on 9th Maths Chapter 2

=x^2 + (4 + 10)x + 4 × 10

[∵〖(x + a)(x + b) = x〗^2 + (a + b) x + ab]

= x^2 + 14x + 40

Putting x + 1 = 0,

we get, x = – 1

Using remainder theorem,

when p(x)=x^3+x^2+x+1 is divided by x + 1,

remainder is given by p(-1)

=〖(-1)^3 + (-1)〗^2 + (-1) + 1

= – 1 + 1 – 1 + 1

= 0

Since, remainder p(-1) = 0,

Hence x + 1 is a factor of x^3 + x^2 + x + 1.

g(x) = x + 1

Putting x + 1 = 0,

we get, x = -1

Using remainder theorem,

when p(x) = 2x^3 + x^2 – 2x – 1 is divided by g(x) = x + 1, remainder is given by p(-1)

=〖(-1)^3 + (-1)〗^2 + (-1) + 1

= – 1 + 1 – 1 + 1

= 0

Since, remainder p(-1) = 0,

hence g(x) is a factor of p(x).

= (100 + 3)(100 + 7)

= (100)^2 + (3 + 7)100 + 3 × 7

[∵〖(x + a)(x + b) = x〗^2 + (a + b)x + ab]

= 10000 + 1000 + 21

= 11021

=(3x)^2 + 2 × 3x × y + y^2

=(3x + y)^2

[∵a^2 + 2ab + b^2 = (a + b)^2]

= (100)^3 + (-1)^3 + 3(100)^2 (-1) + 3(100) (-1)^2

[〖∵(a + b)〗^3 = a^3 + b^3 + 3a^2 b + 3ab^2 ]

= 1000000 – 1 -30000 + 300

= 970299

Putting x – 1 = 0, we get, x = 1

Using remainder theorem,

When p(x) = x^2 + x + k is divided by x – 1, remainder is given by p(1)

= (1)^2 + (1) + k

= 2 + k

Since x – 1 is a factor of p(x), hence remainder p(1) = 0

⇒ 2 + k = 0

⇒ k = -2

x – a = 0 रखने पर, x = a

शेषफल प्रमेय के अनुसार

p(x) =〖x^3 – ax〗^2 + 6x – a को x – a से भाग देने पर शेषफल

p(a) =〖(a)^3 – a(a)〗^2 + 6(a) – a

= a^3 – a^3 + 6a – a

= 5a

Putting p(x) = 0, we get

x + 5 = 0

⇒ x = – 5

Hence, x = – 5 is a zero of the polynomial p(x).