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Exercise 2.4 - Chapter 2 Polynomials class 9 ncert solutions Maths - SaraNextGen [2024]


Question 1:

Find the remainder when x3 + 3x2 + 3x + 1 is divided by

(i) x + 1 (ii) https://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1671/Chapter%202_html_188a6c9b.gif  (iii) x

(iv) x + π (v) 5 + 2x

Answer:

(i) x + 1

By long division,

https://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1671/Chapter%202_html_13c54cc9.gif

Therefore, the remainder is 0.

(ii) https://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1671/Chapter%202_html_188a6c9b.gif

By long division,

https://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1671/Chapter%202_html_m2b762df.gif

Therefore, the remainder ishttps://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1671/Chapter%202_html_m53aaaaf8.gif .

(iii) x

By long division,

https://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1671/Chapter%202_html_m117372ad.gif

Therefore, the remainder is 1.

(iv) x + π

By long division,

https://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1671/Chapter%202_html_18b3d937.gif

Therefore, the remainder is https://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1671/Chapter%202_html_2ccb3c71.gif

(v) 5 + 2x

By long division,

https://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1671/Chapter%202_html_3624a95e.gif

Therefore, the remainder ishttps://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1671/Chapter%202_html_m36558aad.gif

 

Question 2:

Find the remainder when x3 − ax2 + 6x − is divided by x − a.

Answer:

By long division,

https://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1674/Chapter%202_html_5c63e6d1.gif

Therefore, when x3 − ax2 + 6x − is divided by x − a, the remainder obtained is 5a.

 

Question 3:

Check whether 7 + 3x is a factor of 3x3 + 7x.

Answer:

Let us divide (3x3 + 7x) by (7 + 3x). If the remainder obtained is 0, then 7 + 3will be a factor of 3x3 + 7x.

By long division,

https://img-nm.mnimgs.com/img/study_content/curr/1/9/7/99/1678/Chapter%202_html_m34a169ca.gif

As the remainder is not zero, therefore, 7 + 3x is not a factor of 3x3 + 7x.

Also Read : Exercise-2.5-Chapter-2-Polynomials-class-9-ncert-solutions-Maths

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