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x2 - 16x + ____
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what do you want
to fill in the blank at the end of the trinomial
|\[(b/2)^{2}\]
I'm assuming you want this trinomial to be a perfect square. In that case, notice that every perfect square trinomial with a negative sign is of the form\[a^2x^2-2abx+b^2\]In this case, we have that \(a=1\), so we want a polynomial of the form \[x^2-2bx+b^2\]Fortunately, \(-16=2(-8)\), let \(b=-8\). In that case the last number should be \[b^2 =(-8)^2=64\]
thx
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\[(16/2)^{2}=64\rightarrow is x ^{2}-16x+64\]
You're welcome.
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