91Ó°ÊÓ

Simplify each power of i to \(i, 1,-i,\) or \(-1\). $$i^{102}$$

Use Descartes' rule of signs to determine the possible numbers of positive and negative real zeros for \(P(x) .\) Then, use a graph to determine the actual numbers of positive and negative real zeros. $$P(x)=5 x^{4}+3 x^{2}+2 x-9$$

Simplify each power of i to \(i, 1,-i,\) or \(-1\). $$i^{-6}$$

Concept Check For each pair of numbers, find the values of \(a, b,\) and \(c\) for which the quadratic equation ax \(^{2}+b x+c=0\) has the given numbers as solutions. Answers may vary. (Hint: Use the zero-product property in reverse.) $$2 i,-2 i$$

Factor \(P(x)\) into linear factors given that \(k\) is a zero of \(P\). $$P(x)=x^{3}-2 x^{2}-7 x-4 ; \quad k=-1$$

Concept Check For each pair of numbers, find the values of \(a, b,\) and \(c\) for which the quadratic equation ax \(^{2}+b x+c=0\) has the given numbers as solutions. Answers may vary. (Hint: Use the zero-product property in reverse.) $$1+\sqrt{3}, 1-\sqrt{3}$$

Factor \(P(x)\) into linear factors given that \(k\) is a zero of \(P\). $$P(x)=x^{3}+x^{2}-21 x-45 ; \quad k=-3$$

Simplify each power of i to \(i, 1,-i,\) or \(-1\). $$i^{-15}$$

Use Descartes' rule of signs to determine the possible numbers of positive and negative real zeros for \(P(x) .\) Then, use a graph to determine the actual numbers of positive and negative real zeros. $$P(x)=3 x^{4}+2 x^{3}-8 x^{2}-10 x-1$$

Divide. $$\frac{3 x^{4}-7 x^{3}+6 x-16}{3 x-7}$$