Question

determine which of the following polynomials has (x+1)a factor. (I) x4+x3+x2+x+1​

Answer 1

Step-by-step explanation:

assume that,

( x+ 1 ) = ( x - 1 )

place ( x = -1 ) in equation.

x4 + x3 + x2 + x + 1 =

( -1 * 4 ) + ( -1 * 3 ) + ( -1 * 2 ) + ( -1 ) + 1 = 0

(-4) + (-3) +( -2 )+ ( -1 ) + 1 = 0

( -7 ) + ( -3 ) + 1 = 0

(-10 )+ 1 = 0

( -9 ) = 0

Ans - The polynomials has no factor.

Answer 2

The zero of x + 1 is -1.  

(I) Let p (x) = x4 + x3 + x2 + x + 1

∴ P(-1) = (-1)4 + (-1)3 + (-1)2 + (-1)+1

= 1 – 1 + 1 – 1 + 1

⇒ P (-1) ≠ 1

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