To divide the expressions 3x3, 2x2, 61x, and 20 by 5x, we will work through each term step by step.
1. Dividing 3x3 by 5x:
To divide these two, we can apply the rules of division for algebraic expressions. We separate the coefficients and the variable. So:
- Coefficients: 3 / 5 gives us 3/5
- Variables: x3 / x becomes x(3-1) = x2
Putting it together, we get: 3x2 / 5
2. Dividing 2x2 by 5x:
Using the same approach:
- Coefficients: 2 / 5 results in 2/5
- Variables: x2 / x becomes x(2-1) = x
Thus, we have: 2x / 5
3. Dividing 61x by 5x:
Again, we apply the same rules:
- Coefficients: 61 / 5 stays as 61/5
- Variables: x / x simplifies to 1, since anything divided by itself equals 1.
So we end up with: 61 / 5
4. Dividing 20 by 5x:
Here, we only consider the coefficients since there’s no x in the numerator:
- 20 / 5 gives us 4, and since there is still an x in the denominator, the result is expressed as:
- 4 / x
Summing it all up:
After performing all the divisions, we have:
- 3x2 / 5
- 2x / 5
- 61 / 5
- 4 / x
So, the results of dividing each term by 5x are shown above. Each expression gives you a clearer understanding of how the division simplifies the expressions while maintaining the correct variables and coefficients.