Question

find the remainder when x³ +3x³+3x+1 is divided by.
question 1.= x+n
question 2.= 5+2x
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Answer 1

Answer:

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

(i) x + 1 (ii) x –1/2 (iii) x (iv) x + π (v) 5 + 2x

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

(i) x + 1 (ii) x –1/2 (iii) x (iv) x + π (v) 5 + 2x

Solution: (i) x + 1

Apply remainder theorem

=>x + 1 =0

=> x = - 1

Replace x by – 1 we get

=>x3+3x2 + 3x + 1

=>(-1)3 + 3(-1)2 + 3(-1) + 1

=> -1 + 3 - 3 + 1

=> 0

Remainder is 0

(ii) x –1/2

Apply remainder theorem

=>x – 1/2 =0

=> x = 1/2

Replace x by 1/2 we get

=>x3+3x2 + 3x + 1

=>(1/2)3 + 3(1/2)2 + 3(1/2) + 1

=> 1/8 + 3/4 + 3/2 + 1

Add the fraction taking LCM of denominator we get

=>(1 + 6 + 12 + 8)/8

=>27/8

Remainder is 27/8

(iii) x

Apply remainder theorem

=>x =0

Replace x by 0 we get

=>x3+3x2 + 3x + 1

=>(0)3 + 3(0)2 + 3(0) + 1

=> 0+0 +0 + 1

=> 1

Remainder is 1