Question

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determine the gcf of $6x^2y - 12xy + 9x^3y^2$
a $36x^3y^2$
b $3x^3y^2$
c $36xy$
d $3xy$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 6, -12, 9. Prime factors:
6 = 2×3, -12 = -1×2²×3, 9 = 3².
GCF of 6, 12, 9 (ignoring sign) is 3.

Step2: Find GCF of x-terms

Terms: \(x^2\), \(x\), \(x^3\).
Lowest power of \(x\) is \(x^1\) (i.e., \(x\)).

Step3: Find GCF of y-terms

Terms: \(y\), \(y\), \(y^2\).
Lowest power of \(y\) is \(y^1\) (i.e., \(y\)).

Step4: Combine GCFs

Multiply coefficient GCF (3), \(x\)-GCF (\(x\)), and \(y\)-GCF (\(y\)): \(3 \times x \times y = 3xy\).

Answer:

D. \(3xy\)