Question

Which of the following is a root of the polynomial shown below? f(x)=x^3-x^2-9x+9

Answer 1

Answer:

-3 is the best answer i hope it helps

Step-by-step explanation:

Answer 2

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.