Question

find the remainder when x^3+3x^2+3x+1 is divided by (use remainder theorem)
1)x+1
2)x-1/2
3)x
4)x+π
5)5+2x

Answer 1

Question:-

find the remainder when x^3+3x^2+3x+1 is divided by (use remainder theorem)

1)x+1

2)x-1/2

3)x

4)x+π

5)5+2x

Answer :-

solution 1 St =p(-1)=0

solution 2nd=p(1/2)=27/8

solution 3rd= (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

Solution 4th :-

(iv) x + π

Apply remainder theorem

=>x + π =0

=> x = - π

Replace x by – π we get

=>x3+3x2 + 3x + 1

=>(- π)3 + 3(-π)2 + 3(-π) + 1

=> - π3 + 3π2 - 3π + 1

Remainder is - π3 + 3π2 - 3π + 1

solution 5th :-. (v) 5 + 2x

Apply remainder theorem

=>5+2x =0

=> 2x = - 5

=> x = - 5/2

Replace x by – 5/2 we get

=>x3+3x2 + 3x + 1

=>(-5/2)3 + 3(-5/2)2 + 3(-5/2) + 1

=> -125/8 + 75/4 – 15/2 + 1

Add the fraction taking LCM of denominator

=>(-125 + 150 - 60 + 8 )/125

=> -27/8

Remainder is -27/8

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Answer 2

Step-by-step explanation:

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