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f(x) = x^3 + 6x^2 + 3x - 20   (x + 4) is a factor Use synthetic division and solve...

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kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted August 3, 2013 at 12:22 AM via web

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f(x) = x^3 + 6x^2 + 3x - 20   (x + 4) is a factor

Use synthetic division and solve the resulting quadratic quotient to find all zeros.

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llltkl | College Teacher | (Level 3) Valedictorian

Posted August 3, 2013 at 1:19 AM (Answer #1)

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Given: (x+4) is a factor of the given polynomial `x^3 + 6x^2 + 3x - 20.` Then -4 is a root.

Using synthetic division:

-4 |   1     +6      +3      -20

                -4       -8      -20

      -------------------------

         1      2        -5        0

The resulting quotient is `x^2+2x-5` . Since, this is a quadratic function its roots are:

`(-2+-sqrt(2^2-4*1*-5))/(2*1)`

`=(-2+-sqrt24)/2`

`=-1+-sqrt6`

Therefore, the zeroes of f(x) are `-4,-1-sqrt6, -1+sqrt6.`

The graph:

 

Sources:

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