arpitha factors out the greatest common factor, 9n, from the terms of the polynomial shown. 162m³n⁴ + 45n =…

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

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

Answer

Explanation:

Step1: Divide the first term of the polynomial by the GCF

We have the polynomial (162m^{3}n^{4}+45n) and the GCF (9n). To find the first term in the parentheses, divide (162m^{3}n^{4}) by (9n). Using the rule (\frac{a^{m}}{a^{n}}=a^{m - n}) and (\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: Check the second - term division (for verification)

Divide (45n) by (9n). (\frac{45n}{9n}=\frac{45}{9}\times\frac{n}{n}=5) (since (\frac{n}{n} = 1) for (n\neq0)).

Answer:

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