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Chapter 6: Problem 43

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. $$6 x^{3} y^{2}+9 x y$$

Short Answer

Expert verified
The factored form of the polynomial \(6x^{3}y^{2} + 9xy\) is \(3xy(2x^{2}y + 3)\)

Step by step solution

01

Determine the GCF

In the polynomial \(6x^{3}y^{2}+9xy\), first determine the greatest common factor of the coefficients and the variables. The GCF of 6 and 9 is 3; the smallest power for \(x\) is 1 and \(y\) is also 1. So the GCF is \(3xy\).
02

Divide each term by the GCF

Now, divide each term of the polynomial by the GCF. This gives: \((6x^{3}y^{2} 梅 3xy) + (9xy 梅 3xy)\).
03

Simplify

Simplify equation, which yields \(2x^{2}y + 3\).
04

Write the factored form

Combine the GCF and the simplified polynomial to get the factored form. So, \(6x^{3}y^{2}+9xy = 3xy(2x^{2}y + 3)\)

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Most popular questions from this chapter

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