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Chapter 2: Problem 27
Perform the operation and write the result in standard form. $$(-2+\sqrt{-8})+(5-\sqrt{-50})$$
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Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=x^{4}+10 x^{2}+9$$
Match the cubic function with the numbers of rational and irrational zeros. (a) Rational zeros: \(0 ;\) irrational zeros: 1 (b) Rational zeros: \(3 ;\) irrational zeros: 0 (c) Rational zeros: \(1 ;\) irrational zeros: 2 (d) Rational zeros: \(1 ;\) irrational zeros: 0 $$f(x)=x^{3}-x$$
Write the polynomial (a) as the product of factors that are irreducible over the rationals, (b) as the product of linear and quadratic factors that are irreducible over the reals, and (c) in completely factored form. $$f(x)=x^{4}+6 x^{2}-27$$
Determine (if possible) the zeros of the function \(g\) when the function \(f\) has zeros at \(x=r_{1}, x=r_{2},\) and \(x=r_{3}\) $$g(x)=f(-x)$$
Write the polynomial as the product of linear factors and list all the zeros of the function. $$h(x)=x^{2}-2 x+17$$
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