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Chapter 6: Problem 53

Factor each polynomial using the negative of the greatest common factor. $$-4 a^{3} b^{2}+6 a b$$

Short Answer

Expert verified
The factored form of the polynomial \( -4a^{3}b^{2} + 6ab \) using the negative of the GCF is \( -2ab (2a^{2}b - 3) \).

Step by step solution

01

Identify the GCF

The given polynomial is \( -4a^{3}b^{2} + 6ab \). The greatest common factor (GCF) of these terms is \( 2ab \).
02

Subtract the GCF

Factor out the negative of the GCF, which is \( -2ab \). After doing this, you'll get \( -2ab (2a^{2}b - 3) \). See that the polynomial is the product of the GCF and the resulting expression. Therefore, the factored form using the negative of the GCF is \( -2ab (2a^{2}b - 3) \).

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Most popular questions from this chapter

Factor completely. $$6 x^{4}+35 x^{2}-6$$

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. $$20 a^{4}-45 a^{2}$$

Describe a strategy that can be used to factor polynomials.

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. $$2 y^{3}+3 y^{2}-50 y-75$$

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.
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