Question

determine which of the following polynomiAl has (x+1) as factors
i) x³-x²-x+1
ii)x⁴-x³+x²-x+1
iii)x⁴+2x³+2x²+x+1
iv)x³-x²-(3ROOT3)x +root3
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Answer 1

Answer:

Apply remainder theorem

x+1=0

x=−1

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

Step-by-step explanation:

plz check ans using this formula

Answer 2

Answer:

Apply remainder theorem 

x+1=0

x=−1

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

(i) x3+x2+x+1=(−1)3+(−1)2+(−1)+1=−1+1−1+1=0

Then x+1 is the factor of equation

(ii) x4+x3+x2+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) x4+3x3+3x2+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)x3−x2−(2+2)x+2