NCERT solution class 9 chapter 2 Polynomials exercise 2.4 mathematics

EXERCISE 2.4


Page No 40:

Question 1:

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

(i) x + 1 (ii)  (iii) x

(iv) x + π (v) 5 + 2x

Answer:

(i) x + 1

By long division,

Therefore, the remainder is 0.

(ii) 

By long division,

Therefore, the remainder is.

(iii) x

By long division,

Therefore, the remainder is 1.

(iv) x + π

By long division,

Therefore, the remainder is 

(v) 5 + 2x

By long division,

Therefore, the remainder is


Question 2:

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

Answer:

By long division,

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,

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


 

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