NCERT Solutions for Exercise 2.4 Class 9 Maths Chapter 2 - Polynomials

NCERT Solutions for Exercise 2.4 Class 9 Maths Chapter 2 - Polynomials

NCERT Solutions for exercise 2.4 Class 9 Maths chapter 2 Polynomials exercise 2.4 is the part of NCERT solutions for Class 9 Maths. A polynomial expression is an equation made up of variables (or indeterminate variables), terms, exponents, and constants. If we talk about exercise 2.4 Class 9 Maths is an exercise of the chapter introduced and followed by exercise 2.3 that includes some numerical problems. Here in this exercise 2.4, we will be studying the factorisation of Polynomials.

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The Class 9 Maths chapter 2 exercise 2.4 lists some basic level practice problems on the polynomials chapter that consist of factorization of higher degree Polynomials. The Class 9 Maths chapter 2 exercise 2.4 covers the topics like factorization theorem enclosed with examples. NCERT solutions for Class 9 Maths chapter 2 exercise 2.4 gives an end-to-end idea of the whole chapter. Along with Class 9 Maths chapter 1 exercise 2.4 the following exercises are also present.

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  • Polynomials Exercise 2.1

  • Polynomials Exercise 2.2

  • Polynomials Exercise 2.3.

  • Polynomials Exercise 2.5

Polynomials Class 9 Chapter 2 Exercise: 2.4

Q1 (i) Determine which of the following polynomials has a factor :

Answer:

Zero of polynomial is -1.

If is a factor of polynomial

Then, must be equal to zero

Now,





Therefore, is a factor of polynomial

Q1 (ii) Determine which of the following polynomials has a factor :

Answer:

Zero of polynomial is -1.

If is a factor of polynomial

Then, must be equal to zero

Now,





Therefore, is not a factor of polynomial

Q1 (iii) Determine which of the following polynomials has a factor :

Answer:

Zero of polynomial is -1.

If is a factor of polynomial

Then, must be equal to zero

Now,





Therefore, is not a factor of polynomial

Q1 (iv) Determine which of the following polynomials has a factor :

Answer:

Zero of polynomial is -1.

If is a factor of polynomial

Then, must be equal to zero

Now,





Therefore, is not a factor of polynomial

Q2 (i) Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:

Answer:

Zero of polynomial is

If is factor of polynomial

Then, must be equal to zero

Now,





Therefore, is factor of polynomial

Q2 (ii) Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:

Answer:

Zero of polynomial is

If is factor of polynomial

Then, must be equal to zero

Now,





Therefore, is not a factor of polynomial

Q2 (iii) Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:

Answer:

Zero of polynomial is

If is factor of polynomial

Then, must be equal to zero

Now,





Therefore, is a factor of polynomial

Q3 (i) Find the value of k , if is a factor of p(x) in the following case:

Answer:

Zero of polynomial is

If is factor of polynomial

Then, must be equal to zero

Now,









Therefore, value of k is

Q3 (ii) Find the value of k , if is a factor of p(x) in the following case:

Answer:

Zero of the polynomial is

If is factor of polynomial

Then, must be equal to zero

Now,









Therefore, value of k is

Q3 (iii) Find the value of k , if is a factor of p(x) in the following case:

Answer:

Zero of polynomial is

If is factor of polynomial

Then, must be equal to zero

Now,









Therefore, value of k is

Q3 (iv) the value of k , if is a factor of p(x) in the following case:

Answer:

Zero of polynomial is

If is factor of polynomial

Then, must be equal to zero

Now,








Therefore, value of k is

Q4 (i) Factorise :

Answer:

Given polynomial is

We need to factorise the middle term into two terms such that their product is equal to and their sum is equal to

We can solve it as







Q4 (ii) Factorise :

Answer:

Given polynomial is

We need to factorise the middle term into two terms such that their product is equal to and their sum is equal to

We can solve it as







Q4 (iii) Factorise :

Answer:

Given polynomial is

We need to factorise the middle term into two terms such that their product is equal to and their sum is equal to

We can solve it as







Q4 (iv) Factorise :

Answer:

Given polynomial is

We need to factorise the middle term into two terms such that their product is equal to and their sum is equal to

We can solve it as







Q5 (i) Factorise :

Answer:

Given polynomial is

Now, by hit and trial method we observed that is one of the factors of the given polynomial.

By long division method, we will get

We know that Dividend = (Divisor Quotient) + Remainder







Therefore, on factorization of we will get

Q5 (ii) Factorise :

Answer:

Given polynomial is

Now, by hit and trial method we observed that is one of the factors of the given polynomial.

By long division method, we will get

We know that Dividend = (Divisor Quotient) + Remainder







Therefore, on factorization of we will get

Q5 (iii) Factorise :

Answer:

Given polynomial is

Now, by hit and trial method we observed that is one of the factore of given polynomial.

By long division method, we will get

We know that Dividend = (Divisor Quotient) + Remainder







Therefore, on factorization of we will get

Q5 (iv) Factorise :

Answer:

Given polynomial is

Now, by hit and trial method we observed that is one of the factors of the given polynomial.

By long division method, we will get

We know that Dividend = (Divisor Quotient) + Remainder







Therefore, on factorization of we will get

More About NCERT Solutions For Class 9 Maths Chapter 2 Exercise 2.4

The problems from the concepts of factorization of polynomials are covered in exercise 2.4 Class 9 Maths. The Initial questions of NCERT solutions for Class 9 Maths chapter 2 exercise 2.4 is to determine the factor of given polynomial expression. And later on questions of Class 9 Maths chapter 2 exercise, 2.4 is to factorize the given polynomial expression using splitting the middle term, the concept of division of polynomials will also be discussed in Class 9 Maths chapter 2 exercise 2.4.

Also Read| Polynomials Class 9 Notes

Also see-

  • NCERT Solutions for Class 9 Maths Chapter 2
  • NCERT Exemplar Solutions Class 9 Maths Chapter 2

NCERT Solutions of Class 10 Subject Wise

  • NCERT Solutions for Class 9 Maths

  • NCERT Solutions for Class 9 Science

Subject Wise NCERT Exemplar Solutions

  • NCERT Exemplar Class 9 Maths
  • NCERT Exemplar Class 9 Science