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 \(162m^{3}n^{4}\) by \(9n\). Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\) and dividing coefficients: \(\frac{162}{9}=18\), \(\frac{m^{3}}{1}=m^{3}\), \(\frac{n^{4}}{n}=n^{4 - 1}=n^{3}\). So \(\frac{162m^{3}n^{4}}{9n}=18m^{3}n^{3}\).

Step2: Verify with the second term

Check the second term: \(\frac{45n}{9n} = 5\), which matches the given factored form. So the missing term is \(18m^{3}n^{3}\).

Answer:

C. \(18m^{3}n^{3}\)