Question

pls answer all of them i will mark you as a brainliest

Answer 1

Given f(x) = x^3 + x^2 - 4x - 4.

= > The constant term in f(x) is -4 and the factors of -4 are +1,-1,+2,-2,+4,-4.

Substitute x = +1,-1 in f(x), we get

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

           = 1 + 1 - 4 - 4

           = 2 - 4 - 4

           = -6.


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

            = -1 + 1 + 4 - 4

            = 0.


(x + 1) is a factor of f(x).


Now,

Substitute x = -2,+2 in f(x), we get

= > f(-2) = (-2)^3 + (-2)^2 - 4(-2) - 4

            = -8 + 4 + 8 - 4

           = 0.


(x + 2) is  a factor of f(x). 


= > f(2) = (2)^3 + (2)^2 - 4(2) - 4

             = 8 + 4 - 8 - 4

             = 0.


Therefore (x - 2) is a factor.

 (x + 3) & (x - 3) cannot be factors of f(x).


Hence, (x + 1)(x - 2)(x + 2) a factors of x^3 + x^2 - 4x - 4.


Hope this helps!