# 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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### 1 Answer

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:

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