Part A) 2y(x³+6x-2x²-12)
Part B) 2y(x²+6)(x-2)
Explanation:
Part A) The GCF of the coefficients is 2, as the smallest coefficient is 2 and they are all even. The only variable that is in all 4 terms is y, so the GCF is 2y. Factoring this out of the first term leaves us with x³; from the second term leaves us 6x; from the third term leaves us -2x²; and from the last term leaves us -24.
Part B) Once the GCF is factored out, we group the remaining factor in parentheses, the first two terms together and the last two together:
2y[(x³+6x)+(-2x²-12)]
Take the GCF out of each group:
2y[x(x²+6)+-2(x²+6)]
Factor out what both have in common, x²+6:
2y(x²+6)(x-2)
