Question

Determine which of the
following polynomials
has (x+1) as a
factor
(iii)x*4+2x*3+2x*2+x+1​

Answer 1

Answer:

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

Step-by-step explanation:

If (x+1) is a factor

Then, -1 is a factor

Substitute -1 in the equation x^4+2x^3+2x^2+x+1

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

=1+2(-1)+2(1)-1+1

=1-2+2-1+1

=1

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

Answer 2

$x+1=0\\\\x=-1$

Put value of x in given polynomial :

$x^4+2x^3+2x^2+x+1\\\\=(-1)^4+2(-1)^3+2(-1)^2+(-1)+1\\\\=1-2+2-1+1\\\\=1$

As the value is not zero hence ( x + 1 ) is not a factor of x⁴ + 2x³ + 2x² + x + 1 .