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What are the zeros of the polynomial function
F(x) = x3 + x2 - 6x?
A. x= -3, x = 0, and x = 2
B. x = -2, x = 0, and x = 3
C. x= -1, x = 0, and x = 6
D. x= -6, x = 0, and x = 1

Respuesta :

Cricetus

Answer:

x=0, x= -3 and x=2

Step-by-step explanation:

[tex]f(x)=x^3+x^2-6x[/tex]

put f(x)=0

[tex]f(x)=0[/tex]

[tex]x^3+x^2-6x=0[/tex]

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

Splitting the middle term in such a way that their product is [tex]-6x^2[/tex] and sum is [tex]x[/tex]

[tex]x(x^2+3x-2x-6)=0[/tex]

[tex]x[x(x+3)-2(x+3)]=0[/tex]

[tex]x(x+3)(x-2)=0[/tex]

hence

[tex]x=0[/tex]

[tex](x+3)=0[/tex]

[tex]x=-3[/tex]

[tex](x-2)=0[/tex]

[tex]x=2[/tex]

hence the zeros of the polynomial are 0,-3,2

Answer:

C

Step-by-step explanation:

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