Question

factor $18n^{5}p^{2}-20np^{5}+10n^{2}p+12np$.

a. $18n^{5}p^{2}-20np^{5}+10n^{2}p+12np$

b. $2np(9n^{4}p-10p^{4}+5n+6)$

c. $np(18n^{4}p-20p^{4}+10n+12)$

d. $2n(9n^{4}p^{2}-10p^{4}+5np+6)$

Explanation:

Step1: Identify greatest common factor

Find GCF of coefficients: $\gcd(18,20,10,12)=2$; GCF of variables: $\gcd(n^5p^2,np^5,n^2p,np)=np$. Overall GCF: $2np$.

Step2: Factor out GCF from each term

$\frac{18n^5p^2}{2np}=9n^4p$, $\frac{-20np^5}{2np}=-10p^4$, $\frac{10n^2p}{2np}=5n$, $\frac{12np}{2np}=6$

Step3: Combine into factored form

$2np(9n^4p - 10p^4 + 5n + 6)$

Answer:

b. $2np(9n^{4}p - 10p^{4} + 5n + 6)$