Question

dertermine (x+1) is a factor of x^4+3x^3+3x^2+x+1​

Answer 1

$\mathcal{\huge{\underline{\underline{\red{Question ?}}}}}$

⏩ Dertermine (x+1) is a factor of x⁴ + 3x³ + 3x² + x + 1.

$\mathcal{\huge{\underline{\underline{\green{Answer:-}}}}}$

✒ (x+1) is not the factor of x⁴+3x³+3x²+x+1.

$\mathcal{\huge{\underline{\underline{\orange{Solution:-}}}}}$

Given,  x⁴+3x³+3x²+x+1

 

Let p(x)= x⁴+3x³+3x²+x+1

 

The zero of x+1 is -1.

 

On putting x= -1

p(−1)=(−1)⁴+3(−1)³+3(−1)²+(−1)+1

 =1−3+3−1+1

=1≠0

 Hence,by factor theorem, x+1 is not a factor of x⁴+3x³+3x²+x+1

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Answer 2

$\huge \underline \bold \orange {Answer}$

Given, x⁴+3x³+3x²+x+1

Let p(x)= x⁴+3x³+3x²+x+1

The zero of x+1 is -1.

On putting x= -1

p(−1)=(−1)⁴+3(−1)³+3(−1)²+(−1)+1

=1−3+3−1+1

=1≠0

Hence,by factor theorem, x+1 is not a factor of x⁴+3x³+3x²+x+1