Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.
-$$42 x ^ { 8 } y ^ { 6 } z ^ { 2 } - 36 x ^ { 3 } y ^ { 4 } z ^ { 3 } - 36 x ^ { 5 } y ^ { 2 } z ^ { 4 }$$
A) $6 x ^ { 3 } y ^ { 2 } z ^ { 3 } \left( 7 x ^ { 5 } y ^ { 4 } - 6 y ^ { 2 } - 6 x ^ { 2 } z \right)$
B) $6 x ^ { 3 } y ^ { 2 } z ^ { 2 } \left( 7 x ^ { 5 } y ^ { 4 } - 6 y ^ { 2 } z - 6 x ^ { 2 } z ^ { 2 } \right)$
C) $x ^ { 3 } y ^ { 2 } z ^ { 2 } \left( 42 x ^ { 5 } y ^ { 4 } - 36 y ^ { 2 } z - 36 x ^ { 2 } z ^ { 2 } \right)$
D) $6 \left( 7 x ^ { 8 } y ^ { 6 } z ^ { 2 } - 6 x ^ { 3 } y ^ { 4 } z ^ { 3 } - 6 x ^ { 5 } y ^ { 2 } z ^ { 4 } \right)$

Question

Quizplus · Accepted Answer

The greatest common factor (GCF) of the coefficients (42, 36, 36) is 6. The smallest powers of $x$, $y$, and $z$ in the given polynomial are $x^3$, $y^2$, and $z^2$ respectively. Factoring these out, we get the expression in choice B.

Factor the Greatest Common Factor from the Polynomial 42x8y6z2−36x3y4z3−36x5y2z442 x ^ { 8 } y ^ { 6 } z ^ { 2 } - 36 x ^ { 3 } y ^ { 4 } z ^ { 3 } - 36 x ^ { 5 } y ^ { 2 } z ^ { 4 }42x8y6z2−36x3y4z3−36x5y2z4

Factor the Greatest Common Factor from the Polynomial $42 x ^ { 8 } y ^ { 6 } z ^ { 2 } - 36 x ^ { 3 } y ^ { 4 } z ^ { 3 } - 36 x ^ { 5 } y ^ { 2 } z ^ { 4 }$