## EXERCISE 2.4

#### Page No 40:

#### Question 1:

Find the remainder when *x*^{3} + 3*x*^{2} + 3*x* + 1 is divided by

(i) *x* + 1 (ii) (iii) *x*

(iv) *x* + π (v) 5 + 2*x*

#### 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 + 2*x*

By long division,

Therefore, the remainder is

#### Question 2:

Find the remainder when *x*^{3} − *ax*^{2} + 6*x* − *a *is divided by *x − a*.

#### Answer:

By long division,

Therefore, when *x*^{3} − *ax*^{2} + 6*x* − *a *is divided by *x − a*, the remainder obtained is 5*a*.

#### Question 3:

Check whether 7 + 3*x* is a factor of 3*x*^{3} + 7*x*.

#### Answer:

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

By long division,

As the remainder is not zero, therefore, 7 + 3*x* is not a factor of 3*x*^{3} + 7*x*.