Question

Which of the following is a factor of x4 + 5x3 - 4x2 - 8x + 6?
2x+3
x-1
2x-3
x+1

Answer 1

Answer:

x + 1

Step-by-step explanation:

Answer 2

Answer:

The correct option is 2.

Step-by-step 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:

$(2x+3)=0$

$x=-\frac{3}{2}$

$f(-\frac{3}{2})=(-\frac{3}{2})^4+5(-\frac{3}{2})^3-4(-\frac{3}{2})^2-8(-\frac{3}{2})+6=\frac{-45}{16}\neq 0$

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:

$(2x-3)=0$

$x=\frac{3}{2}$

$f(\frac{3}{2})=(\frac{3}{2})^4+5(\frac{3}{2})^3-4(\frac{3}{2})^2-8(\frac{3}{2})+6=\frac{111}{16}\neq 0$

Therefore option 3 is incorrect.

In option 4:

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

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

Therefore option 4 is incorrect.