Respuesta :
Answer:
This is not factorisable. None of the given options are its factors.
Step-by-step explanation:
We have been given with a polynomial [tex]x^2+x-1[/tex]
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
[tex]\frac{1}{2}^2+\frac{1}{2}-1[/tex]
After simplifying we will get [tex]\frac{1}{4}+\frac{1}{2}-1[/tex]
After further simplification we will get [tex]-\frac{1}{4}[/tex]
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
[tex]2^2+2-1[/tex]
After simplifying we will get [tex]4+2-1[/tex]
After further simplification we will get [tex]5[/tex]
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
[tex]1^2+1-1[/tex]
After simplifying we will get [tex]1+1-1[/tex]
After further simplification we will get [tex]1[/tex]
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
[tex]\frac{-3}{2}^2-\frac{3}{2}-1[/tex]
After simplifying we will get [tex]\frac{9}{4}-\frac{3}{2}-1[/tex]
After further simplification we will get [tex]-\frac{1}{4}[/tex]
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.
