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If f(x) = x^3 - 4x^2 - 3x + 18 has a factor of x+2, find the zeros and plot the graph.

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted July 22, 2013 at 6:37 PM via web

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If f(x) = x^3 - 4x^2 - 3x + 18 has a factor of x+2, find the zeros and plot the graph.

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llltkl | College Teacher | Valedictorian

Posted July 22, 2013 at 7:02 PM (Answer #1)

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The given function is:

f(x) = x^3 - 4x^2 - 3x + 18

It has a factor of (x+2). So, one of its zeroes is -2. In order to find the other zeroes, we have to factorize f(x).

`f(x) = x^3 - 4x^2 - 3x + 18`

`=x^3+2x^2-6x^2-12x+9x+18`

`=x^2(x+2)-6x(x+2)+9(x+2)`

`=(x+2)(x^2-6x+9)`

`=(x+2)(x^2-2*x*3+3^2)`

`=(x+2)(x-3)^2`

Therefore, the zeros of the given function are -2 and 3.

 

     

 

 

 

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