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Chapter 6: Problem 82
Factor using the formula for the sum or difference of two cubes. $$x^{3}-64$$
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Use the \([\mathrm{GRAPH}]\) or \([\mathrm { TABLE }]\) feature of a graphing utility to determine if the polynomial on the left side of each equation has been correctly factored. If not, factor the polynomial correctly and then use your graphing utility to verify the factorization. $$\begin{aligned} &-2 x^{3}+10 x^{2}-2 x-10=2(x+5)\left(x^{2}+1\right) ;[-8,4,1] \text { by }\\\ &[-100,100,10] \end{aligned}$$
Exercises 150鈥�152 will help you prepare for the material covered in the next section. Evaluate \(2 x^{2}+7 x-4\) for \(x=\frac{1}{2}\)
Factor completely. $$12 x^{2}(x-1)-4 x(x-1)-5(x-1)$$
Determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. The factorable trinomial \(4 x^{2}+8 x+3\) and the prime trinomial \(4 x^{2}+8 x+1\) are in the form \(a x^{2}+b x+c\) but \(b^{2}-4 a c\) is a perfect square only in the case of the factorable trinomial.
Use the \([\mathrm{GRAPH}]\) or \([\mathrm { TABLE }]\) feature of a graphing utility to determine if the polynomial on the left side of each equation has been correctly factored. If not, factor the polynomial correctly and then use your graphing utility to verify the factorization. $$\begin{aligned} &6 x^{2}+10 x-4=2(3 x-1)(x+2) ;[-5,5,1] \text { by }\\\ &[-20,20,2] \end{aligned}$$
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