Question

Q). Determine which of the following polynomials has (x+1) a factor:
$(i). \: {x}^{4} + {x}^{3} + {x}^{2} + x + 1$
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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given question =>x⁴ + x³+x²+x+1

As we know the definition of FACTOR THEOREM

=>The zero of x+1= -1

=>x+1=0

=>x= -1

Let,

p(x) = x⁴ + x³+x²+x+1 and s(x)= x+1

p( -1)=(-1)⁴ + (-1)³+ (‐1)²+(-1)+1

=> 1 -1+1-1+1

=>1

SO, BY THE FACTOR THEOREM, X+1 IS NOT A FACTOR OF x⁴ + x³+x²+x+1 .