Answer:
answer is `2x²`
Explanation:
To simplify the expression `(10x^3)/(5x-2)`, we can use polynomial long division.Let's first represent the given expression as:```
________________________
5x - 2 | 10x³ + 0x² + 0x + 0
```
To get the first term of the quotient, we divide the first term of the dividend by the first term of the divisor.```
2x²
________________________
5x - 2 | 10x³ + 0x² + 0x + 0
10x² - 4x²
--------------
4x² + 0x
```
Multiply the quotient term obtained in the previous step by the divisor and subtract the result from the dividend.```
2x²
________________________
5x - 2 | 10x³ + 0x² + 0x + 0
10x² - 4x²
--------------
4x² + 0x
4x² - 0x²
----------
0x² + 0x
```
Bring down the next term of the dividend.```
2x²
________________________
5x - 2 | 10x³ + 0x² + 0x + 0
10x² - 4x²
--------------
4x² + 0x
4x² - 0x²
----------
0x² + 0x
0x + 0
------
0
```
The remainder is zero, so we have completely divided `(10x^3)/(5x-2)` by `(5x-2)`.Therefore, the simplified form of `(10x^3)/(5x-2)` is `2x²`.