NCERT Solutions Class 9 Maths Chapter 2 Polynomials

Introduction :

In this chapter we will learn about Polynomials in one variable, coefficient. The degree of a non-zero constant polynomial is zero Polynomials degree is called a linear , quadratic and cubic polynomial. Value putting and Remainder theorem and dividend. Factorisation of polynomials and factor theorem and by splitting the middle term. Algebraic identities, using identity and the expanded form .

Identity I : ( x + y )² = x² + 2xy + y²
Identity II : ( x - y )² = x² - 2xy + y²
Identity III : x² - y² = ( x + y ) ( x - y )
Identity IV : ( x + a ) ( x + b ) = x² + ( a + b ) x + ab
Identity V : ( x + y + z )² = ( x² + y² + z² + 2xy + 2yz + 2zx )
Identity VI : ( x + y )³ = x³ + y³ + 3xy ( x + y )
Identity VII : ( x - y )³ = x³ - y³ - 3xy ( x - y )
Identity VIII : x³ + y³ + z³ - 3xyz = ( x + y + z ) ( x² + y² + z² - xy - yz - zx )

NCERT Class 9 Maths Chapter 2 Polynomials :

NCERT Solutions Class 9 Maths Chapter 2 Polynomials Exercise 2.1

In this exercise-2.1 we will learn about Polynomials. We know variable but i explain variable is x , y , z \(\displaystyle \infty \), coefficient and zero polynomial. The degree of a non - zero constant polynomial is zero. In particular , if \(\displaystyle {{a}_{0}}\,=\,{{a}_{1}}\,=\,{{a}_{2}}\,=\,{{a}_{3}}\,=\,.....\,=\,{{a}_{n}}\,=\,0\) ( all the constants are zero ), we get the zer0 polynomial, which is denoted by 0.

( x + y )² = x² + 2xy + y²
( x - y )² = x² - 2xy + y²
x² - y² = ( x + y ) ( x - y )

In addition to the above, we shall study some more algebraic identity and their use in factorisation and in evaluating some given expressions.

NCERT Solutions Class 9 Maths Chapter 2 Polynomials Exercise 2.2

In this exercise-2.2 we will learn about Polynomials. Zeroes of the polynomial. A zero of a polynomial need to not be 0. 0 may be a zero of a polynomial. Every linear polynomial has one and only one zero. A polynomial can have more than one zero.

NCERT Solutions Class 9 Maths Chapter 2 Polynomials Exercise 2.3

In this exercise-2.3 we will learn about Polynomials. Remainder theorem, is it not a simple way to find the remainder obtained on dividing a polynomial by a linear polynomial? We will now generalise this fact in the form of the following theorem. We will also show you why the theorem is true, by giving you a proof of the theorem.

NCERT Solutions Class 9 Maths Chapter 2 Polynomials Exercise 2.4

In this exercise-2.4 we will learn about Polynomials. Factor theorem , if p(x) is a polynomial of degree n ≥ 1 and a is any real number then

(i) x - a is a factor of p(x), if p(a) = 0, and

(ii) p(a) = 0, if x - a is a factor of p(x).

This actually follows immediately from the Remainder Theorem, but we shall not prove it here. Using by splitting the middle term.

NCERT Solutions Class 9 Maths Chapter 2 Polynomials Exercise 2.5

In this exercise-2.5 we will learn about Polynomials. Algebraic identities with Examples & Solutions.

Identity I : ( x + y )² = x² + 2xy + y²
Identity II : ( x - y )² = x² - 2xy + y²
Identity III : x² - y² = ( x + y ) ( x - y )
Identity IV : ( x + a ) ( x + b ) = x² + ( a + b ) x + ab
Identity V : ( x + y + z )² = ( x² + y² + z² + 2xy + 2yz + 2zx )
Identity VI : ( x + y )³ = x³ + y³ + 3xy ( x + y )
Identity VII : ( x - y )³ = x³ - y³ - 3xy ( x - y )
Identity VIII : x³ + y³ + z³ - 3xyz = ( x + y + z ) ( x² + y² + z² - xy - yz - zx ) .