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If u(x) = x5 – x4 + x2 and v(x) = –x2, which expression is equivalent to (U divided by V) (x)
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\[u(x)=x ^{5}-x ^{4}+x ^{2}\] and\[v(x)=-x^{2}\] Factor \[u(x) = x ^{2}(x ^{3}-x ^{2}+1)\]. (Notice that this is an application of the distributive property.) You can write the division like this so that it looks more familiar: \[\frac{ u(x) }{ v(x) } = - \frac{ x ^{2}( x ^{3}-x ^{2}+1) }{ x ^{2} }\] The x-squareds in the numerator and denominator 'cancel', leaving the expression in the numerator.
a.x3 – x2 b.–x3 + x2 c.–x3 + x2 – 1 d.x3 – x2 + 1
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