Question

problem 6
factor out the greatest common factor in the following polynomial.
$12x^2y^5 - 30x^4y^2 = \boxed{\quad}$

Explanation:

Step1: Find GCF of coefficients

Find GCF of 12 and 30. Factors of 12: 1,2,3,4,6,12. Factors of 30:1,2,3,5,6,10,15,30. GCF is 6.

Step2: Find GCF of \(x\) terms

For \(x^2\) and \(x^4\), GCF is \(x^2\) (lower exponent).

Step3: Find GCF of \(y\) terms

For \(y^5\) and \(y^2\), GCF is \(y^2\) (lower exponent).

Step4: Factor out GCF

GCF is \(6x^2y^2\). Divide each term by \(6x^2y^2\):
\(\frac{12x^2y^5}{6x^2y^2} - \frac{30x^4y^2}{6x^2y^2} = 2y^3 - 5x^2\).
So, \(12x^2y^5 - 30x^4y^2 = 6x^2y^2(2y^3 - 5x^2)\).

Answer:

\(6x^2y^2(2y^3 - 5x^2)\)