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Determine the x intercepts of the polynomial function:g(x)=x^3+2x^2-9x-18Recall that the x intercept is a point (x,0) where our value for y is always zero. List the intercepts (x,0) from smallest to largest and separate them with a comma between each point.Answer:

Determine the x intercepts of the polynomial functiongxx32x29x18Recall that the x intercept is a point x0 where our value for y is always zero List the intercep class=

Respuesta :

We will have the following:

We determine the x-intercepts as follows:

First, we factor the expression; that is:

[tex]x^3+2x^2-9x-18=(x^3+2x^2)+(-9x-18)[/tex][tex]=x^2(x+2)-9(x+2)=(x+2)(x^2-9)[/tex][tex]=(x+2)(x-3)(x+3)[/tex]

Now, we equal the expression to 0, that is:

[tex](x+2)(x-3)(x+3)=0\Rightarrow\begin{cases}x+2=0 \\ \\ x-3=0 \\ \\ x+3=0\end{cases}[/tex][tex]\Rightarrow\begin{cases}x=-2 \\ \\ x=3 \\ \\ x=-3\end{cases}[/tex]

So, the x-intercepts are located at:

[tex](-2,0)[/tex][tex](-3,0)[/tex][tex](3,0)[/tex]

We can see it as follows:

Ver imagen JulietQ60198

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