Question

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Answer 1

Step-by-step explanation:

Answer:1)

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Answer 2

Answer:

i) x^3+x^2+x+1

Step-by-step explanation:

Since,it is given that: x+1 is factor,so:x= -1;

Now,

Put the value of x in all the equations;

i) x^3+x^2+x^1+1

Putting the value of X;

(-1 x -1 x -1)+(-1 x -1)+(-1)+1

-1 + 1 + -1 + 1=0.

So, x+1 is the factor of this polynomial.

ii) x^4+x^3+x^2+x+1

=> 1 + -1 + 1 + -1 + 1=1.

x+1 is not the factor of this polynomial.

iii) x^4+3x^3+3x^2+x+1

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

=> 1-3+3-1+1=1.

x+1 is not the factor of this polynomial.

iv)x^3-x^2-(2+√2)x+√2

=> -1 - 1 - 2x -x√2+√2

=> -2 +2+√2+√2

=> 2√2.

x+1 is not the factor of this polynomial.

So ,the answer is : x+1 is the factor of

(i) x^3+x^2+x+1

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