Which of the following is a root of the polynomial shown below? f(x)=x^3-x^2-9x+9
(Points : 2)
-9
-3
2
9
Answer:
-3 is the best answer i hope it helps
Step-by-step explanation:
We have been given a polynomial function \(f(x)=x^3-x^2-9x+9\). We are asked to choose the root of the function from given choices.
Let us set our polynomial equal to 0.
\(x^3-x^2-9x+9=0\)
Now we will factor our polynomial by grouping method.
\((x^3-x^2)+(-9x+9)=0\)
Let us factor out greatest common factor from each group.
\(x^2(x-1)-9(x-1)=0\)
\((x-1)(x^2-9)=0\)
We can further factor \((x^2-9)\) using difference of squares.
\((x-1)(x^2-3^2)=0\)
\((x-1)(x+3)(x-3)=0\)
Using zero product property, we will get:
\((x-1)=0\text{ (or) }(x+3)=0\text{ (or) }(x-3)=0\)
\(x=1\text{ (or) }x=-3\text{ (or) }x=3\)
Upon looking at our given choices, we can see that \(-3\) is the correct choice, therefore, \(-3\) is root of the given polynomial.