Question

1. factor $18m^6n^4 + 12m^4n - 8m^4$.

a. $m^4(18m^2n^4 + 12n - 8)$
b. $2m^4(9m^2n^4 + 12n - 8)$
c. $2m^4(9m^2n^4 + 6n - 4)$
d. $2m^4n(9m^2n^3 + 6 - 4n)$

Explanation:

Step1: Identify GCF of terms

Find GCF of $18m^6n^4$, $12m^4n$, $8m^4$:

• Coefficients: $\gcd(18,12,8)=2$
• $m$-terms: $\gcd(m^6,m^4,m^4)=m^4$
• $n$-terms: $\gcd(n^4,n,1)=n$

Overall GCF: $2m^4n$

Step2: Divide each term by GCF

$\frac{18m^6n^4}{2m^4n}=9m^2n^3$, $\frac{12m^4n}{2m^4n}=6$, $\frac{-8m^4}{2m^4n}=-4n$

Step3: Factor out GCF

$2m^4n(9m^2n^3 + 6 - 4n)$

Answer:

d. $2m^4n(9m^2n^3 + 6 - 4n)$