Question

determine wheter polynomial
$x ^{3 } + x ^{2} + x + 1$
has (x+1) a factor or not​

Answer 1

Answer:

x^3+x^2+x+1=0

x+1 is factor it satisfies in the equation

x+1=0

x=-1

substitute x=-1

x^3+x^2+x+1=0

(-1)^3+(-1)^2+(-1)+1=0

-2+2=0

0=0✔

therefore x+1 is a factor

Step-by-step explanation:

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Answer 2

Answer:

p(x) = x³ + x² + x + 1

g(x) = (x + 1 )

∴x = -1

p(-1) = (-1)³ + (-1)² + (-1) +1

       = -1 +1 -1+1

       =0

Since the remainder is zero , g(x) is a factor of p(x)

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Step-by-step explanation: