<PRE><B>Question 171899</B>


{{{x=1}}} and {{{x=-8}}} Start with the given solutions.



Get all terms to the left side in each case



{{{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


{{{x^2+7x-8=0}}}



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Answer:


So the polynomial with roots of  {{{1}}} and {{{-8}}} is


{{{y=x^2+7x-8}}}




Notice how if we graph {{{y=x^2+7x-8}}}, we can visually verify our answer


{{{ graph( 500, 500, -10, 10, -10, 10, x^2+7*x-8 ) }}} Graph of {{{y=x^2+7x-8}}} with roots of {{{x=1}}} and {{{x=-8}}}
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