Question

cd: factor by gcf and grouping
determine the gcf of $6x^2y - 12xy + 9x^3y^2$
a $36x^2y^2$
b $36xy$
c $3xy$
d $3x^2y^2

Explanation:

Step 1: 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.

Step 2: Find GCF of \(x\)-terms

Terms: \(x^2y\), \(xy\), \(x^3y^2\).
For \(x\): exponents are 2, 1, 3. GCF exponent is 1 (smallest). So \(x^1 = x\).

Step 3: Find GCF of \(y\)-terms

Terms: \(x^2y\), \(xy\), \(x^3y^2\).
For \(y\): exponents are 1, 1, 2. GCF exponent is 1 (smallest). So \(y^1 = y\).

Step 4: Combine GCFs

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

Answer:

C. \(3xy\)