Question

Which of the following is a factor of x4 + 5x3 - 4x2 - 8x + 6?

2x+3
x-1
2x-3
x+1

Answer 1

x + 1

Explanation:

Answer 2

The correct option is 2.

Explanation:

The given function is

`f(x)=x^4+5x^3-4x^2-8x+6`

If (x-c) is a factor of a function, then f(c)=0.

In option 1:

`(2x+3)=0`

`x=-(3)/(2)`

`f(-(3)/(2))=(-(3)/(2))^4+5(-(3)/(2))^3-4(-(3)/(2))^2-8(-(3)/(2))+6=(-45)/(16)\\eq 0`

Therefore option 1 is incorrect.

In option 2:

`x-1=0\Rightarrow x=1`

`f(1)=(1)^4+5(1)^3-4(1)^2-8(1)+6=0`

Therefore option 2 is correct and (x-1) is a factor of f(x).

In option 3:

`(2x-3)=0`

`x=(3)/(2)`

`f((3)/(2))=((3)/(2))^4+5((3)/(2))^3-4((3)/(2))^2-8((3)/(2))+6=(111)/(16)\\eq 0`

Therefore option 3 is incorrect.

In option 4:

`x+1=0\Rightarrow x=-1`

`f(-)=(-1)^4+5(-1)^3-4(-1)^2-8(-1)+6=6\\eq 0`

Therefore option 4 is incorrect.