Question

Which of the following expressions is a factor of the polynomial x 2 + x - 1?

Answer 1

If x - 1  is a factor then f(1) = 0   ( By the Factor Theorem)

f(1)  = 1^1 + 1 - 1 =  1  so its not  C

If you check the other 3 you'll find that none of them are factors.

Im assuming that x 2   is x squared, right?

Answer 2

Answer:

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

Step-by-step 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

$\frac{1}{2}^2+\frac{1}{2}-1$

After simplifying we will get $\frac{1}{4}+\frac{1}{2}-1$

After further simplification we will get  $-\frac{1}{4}$

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

$\frac{-3}{2}^2-\frac{3}{2}-1$

After simplifying we will get $\frac{9}{4}-\frac{3}{2}-1$

After further simplification we will get  $-\frac{1}{4}$

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.