Problem

Find the greatest common factor (GCF) of the polynomials \(12x^3y^2 - 18x^2y^3 + 24x^4y\)

Answer

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Answer

Multiply the common factors together to find the GCF: \(2 \cdot 3 \cdot x^2 \cdot y = 6x^2y\)

Steps

Step 1 ：Write out each term with its factors: \(12x^3y^2 = 2^2 \cdot 3 \cdot x^3 \cdot y^2\), \(18x^2y^3 = 2 \cdot 3^2 \cdot x^2 \cdot y^3\), \(24x^4y = 2^3 \cdot 3 \cdot x^4 \cdot y\)

Step 2 ：Identify the common factors: the common factors are 2, 3, \(x^2\), and \(y\)

Step 3 ：Multiply the common factors together to find the GCF: \(2 \cdot 3 \cdot x^2 \cdot y = 6x^2y\)

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