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## NCERT Class 9 Maths Textbook Chapter 2 With Answer Book PDF Free Download

### Chapter 2: Polynomials

#### 2.1Introduction

You have studied algebraic expressions, addition, subtraction, multiplication, and division in earlier classes.

You also have studied how to factorize some algebraic expressions. You may recall the algebraic identities :

#### 2.2 Polynomials in One Variable

Let us begin by recalling that a variable is denoted by a symbol that can take any real value. We use the letters x, y, z, etc. to denote variables. Notice that 2x, 3x, – x, –1 2/x are algebraic expressions. All these expressions are of the form (a constant) × x.

Now suppose we want to write an expression which is (a constant) × (a variable) and we do not know what the constant is. In such cases, we write the constant as a, b, c, etc. So the expression will be ax, say.

However, there is a difference between a letter denoting a constant and a letter denoting a variable.

The values of the constants remain the same throughout a particular situation, that is, the values of the constants do not change in a given problem, but the value of a variable can keep changing

#### 2.4 Remainder Theorem

Let us consider two numbers 15 and 6. You know that when we divide 15 by 6, we get the quotient 2 and remainder 3.

Do you remember how this fact is expressed? We write 15 as

15 = (6 × 2) + 3

We observe that the remainder 3 is less than the divisor 6. Similarly, if we divide

12 by 6, we get

12 = (6 × 2) + 0

What is the remainder here? Here the remainder is 0, and we say that 6 is the factor of 12 or 12 is a multiple of 6

Author | NCERT |

Language | English |

No. of Pages | 23 |

PDF Size | 98 KB |

Category | Mathematics |

Source/ Credits | ncert.nic.in |

### NCERT Solutions Class 9 Maths Chapter 2 Polynomials

**(i) 4x ^{2}–3x+7**

Solution:

The equation 4x^{2}–3x+7 can be written as 4x^{2}–3x^{1}+7x^{0}

Since *x* is the only variable in the given equation and the powers of x (i.e., 2, 1, and 0) are whole numbers, we can say that the expression 4x^{2}–3x+7 is a polynomial in one variable.

**(ii) y ^{2}+√2**

Solution:

The equation y^{2}+**√2** can be written as y^{2}+**√**2y^{0}

Since y is the only variable in the given equation and the powers of y (i.e., 2 and 0) are whole numbers, we can say that the expression y^{2}+**√**2 is a polynomial in one variable.

**(iii) 3√t+t√2**

Solution:

The equation 3√t+t√2 can be written as 3t^{1/2}+√2t

Thought is the only variable in the given equation, the powers of *t* (i.e.,1/2) is not a whole number. Hence, we can say that the expression 3√t+t√2 is **not **a polynomial in one variable.

NCERT Class 9 Maths Textbook Chapter 2 With Answer Book PDF Free Download