**Answer:**

B. -3m^7 + 10m^2

**Step-by-step explanation:**

First, we have to write down the division remembering that **÷** is the same as <em>/</em>

So we will write the division in terms of /

**(-6m^7 + 20m^6) / 2m^4**

This is the same equation as if we were using the symbol ÷

Now we have to remember the distribution when we are dividing fractions:

**(a+b)/c = a/c + b/c** ;

we can separate the fraction to make it easier, in this case:

<em>a = -6m^7</em>

<em>b = 20m^6</em>

<em>c = 2m^4</em>

And substituting in the fraction we have:

**(-6m^7 + 20m^6) / 2m^4 = (-6m^7 / 2m^4) + (20m^6 / 2m^4)**

We are going to use the second part:

**(-6m^7 / 2m^4) + (20m^6 / 2m^4)**

Now we are going to solve each parenthesis:

**(-6m^7 / 2m^4)**

To solve division that has variables with an exponent we have to remember the following:

**ax^n / bx^m = (a/b) x^(n-m)**

Where:

<em>a and b are constant</em>

<em>x is the variable </em>

<em>and n and m are exponents</em>

<em> </em>

In the first parenthesis **(-6m^7 / 2m^4)**:

**(a/b) x^(n-m)**

**(-6/2) m^(7-4) **

Now we solve and we have:

**(-3) m^3 ** this is the first part of the division

Now we have to solve the second part of the division **(20m^6 / 2m^4)**:

**(a/b) x^(n-m)**

**(20/2) m^(6-4)**

Now we solve:

**(10) m^2 **this is the second part of the division

Now we have to put the two parts together:

**(-3m^3) + (10 m^2)**