What is the Factor of
21m3n9+27m4n2+12m3n
Answer (1)
Here's how to solve the problem:1. Find the Greatest Common Factor (GCF) of the coefficients:The coefficients are 21, 27, and 12.The GCF of 21, 27, and 12 is 3.2. Find the GCF of the variables:For 'm': The terms have m³, m⁴, and m³. The lowest power of 'm' is m³.For 'n': The terms have n⁹, n², and n. The lowest power of 'n' is n.3. Combine the GCFs:The GCF of the entire expression is 3m³n.4. Factor out the GCF:Divide each term in the original expression by the GCF (3m³n):(21m³n⁹) ÷ (3m³n) = 7n⁸(27m⁴n²) ÷ (3m³n) = 9mn(12m³n) ÷ (3m³n) = 45. Write the factored expression:3m³n (7n⁸ + 9mn + 4)Final answer:Therefore, the factored form of 21m³n⁹ + 27m⁴n² + 12m³n is 3m³n(7n⁸ + 9mn + 4)
