Question

arpitha factors out the greatest common factor, 9n, from the terms of the polynomial shown.
162m³n⁴ + 45n
= 9n(______ + 5)
what is the missing term in the factored expression?
○ 16m³n³
○ 16m³n⁴
○ 18m³n³
○ 18m³n⁴

Explanation:

Step1: Divide the first term by GCF

To find the missing term, divide \(162m^3n^4\) by \(9n\).
\(\frac{162m^3n^4}{9n} = \frac{162}{9}m^3\frac{n^4}{n}\)

Step2: Simplify the division

Simplify \(\frac{162}{9}=18\) and \(\frac{n^4}{n}=n^{4 - 1}=n^3\). So the result is \(18m^3n^3\).

Answer:

18\(m^3n^3\) (corresponding to the option "18\(m^3n^3\)")