Question

pls answer the below questions
find the factors of i)6x²+5x-6
ii)3x²-x-4
iii)12x²-7x+1
iv)x³-2x²-x+2
Class 9 lesson polynomials ​

Answer 1

Mathematics NCERT Grade 9, Chapter 2: Polynomials: Polynomials are a particular type of algebraic expression. Students will also study the remainder theorem and factor theorem in this chapter. Some more algebraic identities will be discussed in this chapter. Their use in factorisation and in evaluating some given expressions will also be discussed. Different polynomials based on the number of terms are discussed in this chapter.

Polynomial with one term is Monomial

Polynomial with two terms is Binomial

Polynomial with three terms is Trinomial

This section also includes the topic degree of a polynomial which refers to the highest power of the variable in a polynomial.

Polynomial of degree 1 is called linear polynomial.

Polynomial of degree 2 is called quadratic polynomial.

Polynomial of degree 3 is called cubic polynomial.

The chapter will move further to the topic zeroes of a polynomial. 3 solved examples are given to make the concept clear to students.

A zero of a polynomial need not to be 0.

0 may be zero of a polynomial.

Every linear polynomial has one and only one zero.

A polynomial can have more than one zero.

Exercise 2.2 is based on the same concept.

The next section explains the topic remainder theorem. In this section, the solved example is given in which each step of the solution is explained in detail.

Remainder Theorem: If p(x) is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial x − a, then the remainder is p(a).

Section 2.5 covers the topic- Factorisation of Polynomials.

Factor theorem: x − a is a factor of polynomial p(x) if p(a) = 0.

Exercise 2.6 is based on the topic- algebraic identities. 8 identities are discussed in this section. These identities are used to solve problems of factorisation. The last exercise of the chapter is Exercise 2.5.

In the end summary of the chapter is given for quick revision of the chapter Polynomials.

Page No 32:

Question 1:

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

(i) (ii) (iii)

(iv) (v)

ANSWER:

(i)

Yes, this expression is a polynomial in one variable x.

(ii)

Yes, this expression is a polynomial in one variable y.

(iii)

No. It can be observed that the exponent of variable t in term is , which is not a whole number. Therefore, this expression is not a polynomial.

(iv)

No. It can be observed that the exponent of variable y in termis −1, which is not a whole number. Therefore, this expression is not a polynomial.

(v)

No. It can be observed that this expression is a polynomial in 3 variables x, y, and t. Therefore, it is not a polynomial in one variable.