# Extra Questions For Class 9 Maths Chapter 2

###### Polynomials | Zeroes of Polynomial | Remainder Theorem | Factorization | Algebraic Identities

Chapter 2 of CBSE NCERT Class 9 Math covers polynomials. Concepts covered in chapter 2 include polynomials in one variable, long division of polynomials, finding zeroes of a polynomial, Remainder Theorem, factorization of polynomials, and useful algebraic identities. The extra questions given below include questions akin to HOTS (Higher Order Thinking Skills) questions and exemplar questions of NCERT.

Here is a quick recap of the key concepts that are covered in the Polynomials Chapter in the CBSE NCERT Class 9 Math text book.

#### What is a polynomial?

A polynomial p(x) is an algebraic expression in a variable x of the form
p(x) = anxn + an - 1xn - 1 + ....... + a1x1 + a0x0, where an ≠ 0

a0, a1, .... an - 1, and an (an ≠ 0) are coefficients of x0, x1, ..... xn - 1, and xn respectively.
'n' is called the degree of the polynomial.

Each of a0x0, a0x0, ..... a0x0, and a0x0 where an ≠ 0 is called a term of the polynomial.

#### What is a zero of a polynomial p(x)?

A real number 'a' is a zero of a polynomial p(x) if p(a) = 0.

In this case 'a' is also called a root of the equation p(x) = 0.

#### What is Remainder Theorem?

If p(x) is a polynomial whose degree is greater than or equal to 1 and if p(x) is divided by (x - a), the remainder of the division is p(a).

#### What is Factor Theorem?

If a polynomial p(x) is divided by (x - a) and p(a) = 0, then (x - a) is a factor of p(x).
Conversely, if (x - a) is a factor of a polynomial p(x), then p(a) = 0

#### Important Algebraic Identities

1. (x + y)2 = x2 + 2xy + y2
2. (x - y)2 = x2 - 2xy + y2
3. x2 - y2 = (x + y)(x - y)
4. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
5. (x + y)3 = x3 + y3 + 3xy(x + y)
Which is the same as (x + y)3 = x3 + 3x2y + 3xy2 + y3
Consequently, x3 + y3 = (x + y)3 - 3xy(x + y)
6. (x - y)3 = x3 - y3 - 3xy(x - y)
Which is the same as (x - y)3 = x3 - 3x2y + 3xy2 - y3
Consequently, x3 - y3 = (x - y)3 + 3xy(x - y)
7. x3 + y3 = (x + y)(x2 - xy + y2)
8. x3 - y3 = (x - y)(x2 + xy + y2)
9. x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz - zx)

### Extra Questions for Class 9 Maths - Polynomials

1. Question 1

Factorize the given expression:
9x2 + 49y2 + 25z2 - 42xy - 30xz + 70yz

2. Question 2

Factorize the given expression:
27x3 - 63x2 + 49x - $$frac{343}{27}$ 3. Question 3 Using suitable identity evaluate the following:$i) 983
(ii) 188 × 212

4. Question 4

If (x - 2a) is a factor of 2x4 - 4ax3 + 7x2 - 13ax - 18, find the value of a.

5. Question 5

Without actual division prove that (x2 - x - 2) divides 2x4 + x3 - 5x2 - 8x - 4

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