Question

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

Answer 1

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

Explanation:

We have been given with a polynomial
`x^2+x-1`

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

`(1)/(2)^2+(1)/(2)-1`

After simplifying we will get
`(1)/(4)+(1)/(2)-1`

After further simplification we will get
`-(1)/(4)`

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

`2^2+2-1`

After simplifying we will get
`4+2-1`

After further simplification we will get
`5`

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

`1^2+1-1`

After simplifying we will get
`1+1-1`

After further simplification we will get
`1`

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

`(-3)/(2)^2-(3)/(2)-1`

After simplifying we will get
`(9)/(4)-(3)/(2)-1`

After further simplification we will get
`-(1)/(4)`

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.