Question

Decide whether (x + 1) is a factor of the polynomial (x^3+x^2-x-1) or not.

Answer 1

Given: (x + 1),  (x^3 + x^2 - x - 1).

To find: Whether (x + 1) is a factor of  (x^3 + x^2 - x - 1).

Answer:

Using factor theorem x + 1 = 0.

x = 0 - 1

x = -1

Let p(x) =  (x^3 + x^2 - x - 1).

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

p(-1) = -1 + 1 + 1 - 1

p(-1) = 0

Therefore, (x + 1) is a factor of  (x^3 + x^2 - x - 1).

Hope it helps :)

Answer 2

PLEASE MAKE AS BRAINLIEST ♥️♥️♥️

x + 1 = 0
x = -1

EQUATION IS ,

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

put value of X in above equation , we get,

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

-1 + 1 + 1 -1 = 0

0 = 0

Hence , (x+1) is the factor of the given equation.