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Chapter 6: Problem 41
Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$11 x^{2}-23$$
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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.
The polynomial \(4 x^{2}+100\) is the sum of two squares and therefore cannot be factored. If the general factoring strategy is used to factor a polynomial, at least two factorizations are necessary before the given polynomial is factored completely.
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. $$8 x^{5}-2 x^{3}$$
Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$16 x^{4} y-y^{5}$$
Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$x y-7 x+3 y-21$$
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