Final answer:
The expression -29x⁴y²+21x⁸y³z³ is factored by first finding the GCF, which is -29x⁴y². The factored form is -29x⁴y²(1 - (3/29)xy²z³).
Step-by-step explanation:
To factor the expression -29x⁴y²+21x⁸y³z³ completely, we first identify the greatest common factor (GCF) of both terms. The GCF is -29x⁴y², which can be divided from both terms of the expression.
So, we factor out -29x⁴y² from each term, which gives us:
-29x⁴y²(1 - (21/29)x⁴yz³). Now, we can simplify the expression inside the parentheses: -29x⁴y²(1 - (3/29)xy²z³).
Since we cannot simplify this any further, the factored form of the expression is:
-29x⁴y² - (29/29)x⁴y² * (3/29)xy²z³ = -29x⁴y²(1 - (3/29)xy²z³).