Question 122093
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<b>This is an answer I posted previously giving the process for solving these problems.</b>


I'll do one of these to show you the process and then you can do the rest.

If -1, 1, 1, and -6 are zeros of a polynomial, then

{{{x=-1}}} => {{{x+1=0}}}
{{{x=1}}}  => {{{x-1=0}}}
{{{x=1}}}  => {{{x-1=0}}}
{{{x=-6}}} => {{{x+6=0}}}

Therefore, the polynomial must be:

{{{(x+1)(x-1)(x-1)(x+6)}}}
{{{(x^2-1)(x^2+5x-6)}}}
{{{x^4+5x^3-6x^2-x^2-5x+6}}}
{{{x^4+5x^3-7x^2-5x+6}}}

And the function would then be {{{f(x)=x^4+5x^3-7x^2-5x+6}}}

Use the same method to solve all of the rest.  The degree of the resulting
polynomial (the highest power on x) must equal the number of roots given
if you have done the work properly.

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