Question

Determine (x + 1) is a factor of x4 + 3x3 + 3x2 + x +1 or not.​

Answer 1

Answer:

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

Step-by-step explanation:

Let p ( x ) = x⁴ + 3x³ + 3x² + x + 1

x + 1 = 0

x = - 1

p ( - 1 ) = ( - 1 )⁴ + 3 ( - 1 )³ + 3 ( - 1 )² + ( - 1 ) + 1

= - 1 + 3 ( - 1 ) + 3 ( 1 ) - 1 + 1

= - 1 - 3 + 3 - 1 + 1

= - 1 - 1 + 1 - 3 + 3

= - 2 + 1 + 0

p ( - 1 ) = - 1

p ( - 1 ) ≠ 0

Therefore,

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

Answer 2

Answer:

step 1:

Put divider = 0

x+1=0

x=-1

step 2:

let p(x) =

putting x=-1

p(-1) =(-1) ^4+3(-1) ^3+3(-1) ^2+x+1

=1-3+3-1+1

=1

this,

Remainder=p(-1) =1

since remainder is not zero,

x+1 is not a factor of x^4+3x^3+3x^2+x+1

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