Question 155167
Start with the given zeros


{{{x=1}}} and {{{x=-8}}}



Get all terms to the left side in each case (ie subtract 1 from both sides in the first equation and add 8 to both sides in the second equation)



{{{x-1=0}}} and {{{x+8=0}}}



Now use the zero product property in reverse to join the factors.



{{{(x-1)(x+8)=0}}}



FOIL and multiply



{{{x^2+7x-8=0}}}



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Answer:


So the polynomial with zeros of  {{{x=1}}} and {{{x=-8}}} is


{{{x^2+7*x-8}}}




Notice how if we graph {{{y=x^2+7*x-8}}}, we can see that the polynomial has roots of {{{x=1}}} and {{{x=-8}}}


{{{ graph( 500, 500, -10, 10, -10, 10, x^2+7*x-8 ) }}} Graph of {{{y=x^2+7*x-8}}} with roots of {{{x=1}}} and {{{x=-8}}}