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

Answer 1

18m³n³

Explanation:

The polynomial given is:

`162m^3n^4+45n`

It has been factored to:

`9n(........... +5 )`

We want to find the missing term. We see that the 45n has already been factored, so we must focus on the first term: 162m³n⁴

Since we are factoring out a 9n, we can divide the term by 9n.

`(162m^3n^4)/(9n)`

According to the exponent rules, when dividing, we subtract the exponents.

`18m^3(n^4)/(n)`

`n^4-n=n^4-n^1=n^3`

`18m^3n^3`

The missing term is 18m³n³.

Answer 2

18m^3n^3

Explanation:

The missing factor (f) is such that ...

9n(f) = 162m^3n^4

Dividing by 9n, we find ...

f = (162m^3n^4)/(9n) = 18m^3n^3