Which of the following expressions is a factor of the polynomial x 2 + x - 1?
a) x -1/2
b) x - 2
c) x - 1
d) x + 3/2

This is not factorisable. None of the given options are its factors.

Step-by-step explanation:

We have been given with a polynomial

In case A we will put x=1/2   since, we need to check (x-1/2) is factor or not of the given polynomial

After substituting x=1/2  in given polynomial we will get

After simplifying we will get

After further simplification we will get  

Option A is not factor of given polynomial since, value at x=1/2 does not satisfying the given polynomial means polynomial is not zero at x=1/2.

In case B  we will put x=2   since, we need to check (x-2) is factor or not of the given polynomial

After substituting x=2  in given polynomial we will get

After simplifying we will get

After further simplification we will get  

Option B is not factor of given polynomial since, value at x=2 does not satisfying the given polynomial means polynomial is not zero at x=2.

In case C we will put x=1 since, we need to check (x-1) is factor or not of the given polynomial

After substituting x=1  in given polynomial we will get

After simplifying we will get

After further simplification we will get  

Option C is not factor of given polynomial since, value at x=1 does not satisfying the given polynomial means polynomial is not zero at x=1.

In case D we will put x=-3/2   since, we need to check (x+3/2) is factor or not of the given polynomial

After substituting x=-3/2  in given polynomial we will get

After simplifying we will get

After further simplification we will get  

Option D is not factor of given polynomial since, value at x=-3/2 does not satisfying the given polynomial means polynomial is not zero at x=-3/2.

The given polynomial is not factorisable

Therefore, None of the options are correct.