# NCERT Solutions for Class 9 Maths Exercise 2.4

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NCERT solutions for Class 9 Maths Polynomials

## NCERT Solutions for Class 9 Maths Polynomials

###### 1. Determine which of the following polynomials hasa factor:

(i)

(ii)

(iii)

(iv)

Ans. (i)

While applying the factor theorem, we get

=-1+1-1+1

=0

We conclude that on dividing the polynomialby, we get the remainder as0.

Therefore, we conclude thatis a factor of.

###### (ii)

While applying the factor theorem, we get

=1-1+1-1+1

=1

We conclude that on dividing the polynomialby, we will get the remainder as1, which is not 0.

Therefore, we conclude thatis not a factor of.

###### (iii)

While applying the factor theorem, we get

=1-3+3-1+1

=1

We conclude that on dividing the polynomialby, we will get the remainder as 1, which is not 0.

Therefore, we conclude thatis not a factor of.

###### (iv)

While applying the factor theorem, we get

We conclude that on dividing the polynomialby, we will get the remainder as, which is not 0.

Therefore, we conclude thatis not a factor of.

NCERT Solutions for Class 9 Maths Exercise 2.4

###### 2. Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the

following cases:

(i)

(ii)

(iii)

Ans. (i)

We know that according to the factor theorem,

We can conclude that g(x) is a factor of p(x), if p(-1)=0.

=2+1-1-2

=0

###### (ii)

We know that according to the factor theorem,

We can conclude that g(x) is a factor of p(x), if p(-2)=0.

=-8+12-6+1

=-1

Therefore, we conclude that the g(x) is not a factor of p(x).

###### (iii)

We know that according to the factor theorem,

We can conclude that g(x) is a factor of p(x), if p(3)=0.

=27-36+3+6

=0

Therefore, we conclude that the g(x) is a factor of p(x).

NCERT Solutions for Class 9 Maths Exercise 2.4

###### 3. Find the value of k, if x – 1 is a factor of p(x) in each of the following cases:

(i)

(ii)

(iii)

(iv)

Ans. (i)

We know that according to the factor theorem

.

We conclude that ifis a factor of, then.

or

###### Therefore, we can conclude that the value of k is.

(ii)

We know that according to the factor theorem

.

We conclude that ifis a factor of, then.

or

Therefore, we can conclude that the value of k is.

(iii)

We know that according to the factor theorem

.

###### We conclude that ifis a factor of, then.

or

Therefore, we can conclude that the value of k is.

(iv)

We know that according to the factor theorem

is a factor of p(x)

We conclude that ifis a factor of, then.

or

Therefore, we can conclude that the value of k is.

NCERT Solutions for Class 9 Maths Exercise 2.4

###### 4. Factorize:

(i)

(ii)

(iii)

(iv)

Ans. (i)

Therefore, we conclude that on factorizing the polynomial, we get.

(ii)

###### Therefore, we conclude that on factorizing the polynomial, we get.

(iii)

Therefore, we conclude that on factorizing the polynomial, we get.

(iv)

Therefore, we conclude that on factorizing the polynomial, we get.

NCERT Solutions for Class 9 Maths Exercise 2.4

###### 5. Factorize:

(i)

(ii)

(iii)

(iv)

Ans. (i)

We need to consider the factors of 2, which are.

Let us substitute 1 in the polynomial, to get

=1-1-2+2=0

###### Thus, according to factor theorem, we can conclude thatis a factor of the polynomial.

Let us divide the polynomialby, to get

Therefore, we can conclude that on factorizing the polynomial, we get .

(ii)

We need to consider the factors of, which are.

Let us substitute 1 in the polynomial, to get

###### Thus, according to factor theorem, we can conclude thatis a factor of the polynomial.

Let us divide the polynomialby, to get

Therefore, we can conclude that on factorizing the polynomial, we get .

(iii)

We need to consider the factors of 20, which are.

Let us substitutein the polynomial, to get

=-1+13-32+20=-20+20=0

###### Thus, according to factor theorem, we can conclude thatis a factor of the polynomial.

Let us divide the polynomialby, to get

Therefore, we can conclude that on factorizing the polynomial, we get.

(iv)

We need to consider the factors of, which are.

Let us substitute 1 in the polynomial, to get

=2+1-2-1=3-3=0

###### Thus, according to factor theorem, we can conclude thatis a factor of the polynomial.

Let us divide the polynomialby, to get

Therefore, we can conclude that on factorizing the polynomial, we get.

## NCERT Solutions for Class 9 Maths Exercise 2.4

NCERT Solutions Class 9 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.

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### 25 thoughts on “NCERT Solutions for Class 9 Maths Exercise 2.4”

2. Que4 me -7x ka split up kar ke -3x and -4x?

3. Nice and it helps me a lot.

5. thank you helped me than normal division u may try L division it make the solving easy.

6. Very help full

9. Thanks

10. What is congruence of triangle

11. Confusing not getting desire answer

12. thank

13. Nice and also easy

14. Nice and very easy

15. Thanks

16. Thank you

17. Thanks, it help me ans lot in my studies and also during the exams, this is too ? good thanks again

18. Nice….. Helped a lot

19. Thanks for this

20. nice and very simple answer.

21. Very -2 nice work
All questions is very simple method
Thanks a lot

22. thanks

23. Help me lots
Thank you very much
Nice ??

24. Thank you very much
Nice

25. Thank you for your help and please continue this do it well never ever giveup