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Chapter 6: Problem 9

Find the greatest common factor of each list of monomials. $$x y, x y^{2},\( and \)x y^{3}$$

Short Answer

Expert verified
The greatest common factor of the monomials \(x y\), \(x y^{2}\), and \(x y^{3}\) is \(xy\).

Step by step solution

01

Factorize the Monomials

The first step to solve this problem is to factorize each of the monomials. For \(x y\), \(x y^{2}\), and \(x y^{3}\) the factorizations will be \(x \cdot y\), \(x \cdot y \cdot y\), and \(x \cdot y \cdot y \cdot y\) respectively.
02

List Common Factors

The next step is to list out the common factors of all three monomials. The factors we have are \(x\), \(y\), \(y^2\), and \(y^3\). Out of these, \(x\) and \(y\) are common to all.
03

Find the Greatest Common Factor

Now, to find the greatest common factor of the monomials, multiply these common factors together. Therefore, the largest common factor of all three monomials is \(x\cdot y\) which can be written as \(xy\).

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Most popular questions from this chapter

Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. \(\frac{x^{2}+6 x+5}{x^{2}-25}\)

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