Problem
Factor out the Greatest Common Factor (GCF) from the polynomial \(12x^3y + 18x^2y^2 + 24x^4y^3\)
Solution
Step 1 ：First, identify the GCF of the coefficients and the variable terms. The GCF of the coefficients 12, 18, and 24 is 6. The GCF of the variable terms \(x^3y, x^2y^2, x^4y^3\) is \(x^2y\).
Step 2 ：Next, divide each term of the polynomial by the GCF. \(\frac{12x^3y}{6x^2y} = 2x, \frac{18x^2y^2}{6x^2y} = 3y, \frac{24x^4y^3}{6x^2y} = 4x^2y^2\).
Step 3 ：Finally, write the factored form of the polynomial. It is the GCF times the result of step 2. \(6x^2y(2x + 3y + 4x^2y^2)\).
