Respuesta :

You have to plug the values in the expression and see if it returns zero.

The only points where the function evaluates to zero are [tex] x=\pm 3[/tex] and [tex]x=6[/tex]

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ANSWER

B. -3,3,-6

EXPLANATION

We equate the given polynomial to zero.

[tex] {x}^{3} + 6 {x}^{2} - 9x - 54 = 0[/tex]

Factor by grouping;

[tex] {x}^{2} (x + 6) - 9(x + 6) = 0[/tex]

Factor further;

[tex]( {x}^{2} - 9)(x + 6) = 0[/tex]

Either

[tex] {x}^{2} - 9 = 0 \: or \: x + 6 = 0[/tex]

[tex] {x}^{2} = 9 \: or \: x = - 6[/tex]

[tex]x = \pm \sqrt{9} \: or \: x = - 6[/tex]

[tex]x = \pm 3 \: or \: x = - 6[/tex]

The zeroes are

x=3,-3,-6

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