How do you divide #(10x^3-11x^2+19x+10)/(5x+2)#?

Question

Ethan Adkins · Accepted Answer

I tried this:

Have a look:

Savannah Anderson · Answer

undefined To divide (10x^3-11x^2+19x+10) by (5x+2), you can use long division or synthetic division. Here is the solution using long division:

2x^2  -3x  + 5
    _______________________
5x + 2 | 10x^3 - 11x^2 + 19x + 10
         - (10x^3 + 4x^2)
         _________________
                      -15x^2 + 19x
                      + ( -15x^2 - 6x)
                      _________________
                                    25x + 10
                                    - (25x + 10)
                                    _________________
                                                 0

Therefore, the quotient is 2x^2 - 3x + 5 and the remainder is 0.

Nathan Axel · Answer

undefined To divide $ \frac{{10x^3 - 11x^2 + 19x + 10}}{{5x + 2}} $, you can use polynomial long division or synthetic division. Here, I'll demonstrate polynomial long division:

1. Divide the highest degree term of the numerator by the highest degree term of the denominator. This gives you the first term of the quotient.
2. Multiply the denominator by the first term of the quotient and subtract it from the numerator.
3. Repeat steps 1 and 2 until the degree of the remainder is less than the degree of the denominator.

Performing polynomial long division:

```
          2x^2  - 3x + 5
      ________________________
5x + 2 | 10x^3 - 11x^2 + 19x + 10
          - (10x^3 + 4x^2)
          _________________
                  -15x^2 + 19x
                  - (-15x^2 - 6x)
                  ______________
                              25x + 10
                              - (25x + 10)
                              ___________
                                      0
```

So, the quotient is $ 2x^2 - 3x + 5 $, and the remainder is $ 0 $. Therefore, $ \frac{{10x^3 - 11x^2 + 19x + 10}}{{5x + 2}} = 2x^2 - 3x + 5 $.