Question

can you give this answer in 2mins. x^3-x^2-(3-√3)x+√3 is a polynomials has (x+1) as a factor​

Answer 1

Apply remainder theorem

x+1=0

x=−1

Put the value of x=−1 in all equations.

(i) x

3

+x

2

+x+1=(−1)

3

+(−1)

2

+(−1)+1=−1+1−1+1=0

Then x+1 is the factor of equation

(ii) x

4

+x

3

+x

2

+x+1=(−1)

4

+(−1)

3

+(−1)

2

+(−1)+1=1−1+1−1+1=1

This is not zero.Then x+1 is not the factor of equation

(iii) x

4

+3x

3

+3x

2

+x+1=(−1)

4

+3(−1)

3

+3(−1)

2

+(−1)+1=1

This is not zero.Then x+1 is not the factor of equation

(iv)x

3

−x

2

−(2+

2

)x+

2

=(−1)

3

−(−1)

2

−(2+

2

)(−1)+

2

=−1−1+2−

2

+

2

=0

This is zero. Then x+1 is the factor of equation