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Chapter 6: Problem 90
Factor each polynomial. $$x^{3}-5+2 x^{3} y-10 y$$
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Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$y^{9}-y^{5}$$
Determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. Multiplying polynomials is relatively mechanical, but factoring often requires a great deal of thought.
Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$24 a^{4} b+60 a^{3} b^{2}+150 a^{2} b^{3}$$
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. $$\begin{aligned} &x^{4}-16=\left(x^{2}+4\right)(x+2)(x-2) ;[-5,5,1] \text { by }\\\ &[-20,20,2] \end{aligned}$$
Factor completely. $$5 y^{5}-5 y^{4}-20 y^{3}+20 y^{2}$$
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