Question

Which of the following is a factor of p(x) = x5 - 4x3 - 2x2 - 4x?

Answer 1

The factor is :
`x(x+2)(x^(3)-2x^(2)-2)`

Explanation:

Given expression is :

`p(x)=x^(5)-4x^(3)-2x^(2)-4x =0`

Taking out x common factor we get

`x^(4)-4x^(2)-2x-4=0`

Further applying rational root theorem we get

`(x+2)(x^(4)-4x^(2)-2x-4)/(x+2)`

Now we will divide
`(x^(4)-4x^(2)-2x-4)/(x+2)` and get

`x^(3)+(-2x^(3)-4x^(2)-2x-4)/(x+2)`

`x^(3)-2x^(2) +(-2x-4)/(x+2)`

`(-2x-4)/(x+2)` = -2

The next factor becomes :
`x^(3)-2x^(2) -2`

Now clubbing all the factors we get the final answer:

`x(x+2)(x^(3)-2x^(2)-2)`

Answer 2

To factor our the following expression we proceed as follows;
p(x)=x^5-4x^3-2x^2-4x
factoring out x we get:
p(x)=x(x^4-4x^2-2x-4)
factoring further we get:
x^4-4x^2-2x-4
=(x+2)(x^3-2x^2-2)
Therefore our expression becomes:
p(x)=x(x+2)(x^3-2x^2-2)
Therefore the factors are x and (x+2) and (x^3-2x^2-2)