Polynomial long division practice worksheet with six problems.

Let’s solve each polynomial long division problem one by one, and write the remainder in fractional form as requested.

---

1) Divide: `(3k² + 10k - 9) ÷ (k - 9)`

We perform polynomial long division:

```
3k + 37
_______________
k - 9 ) 3k² + 10k - 9
3k² - 27k
----------
37k - 9
37k - 333
---------
324
```

✔ Quotient: `3k + 37`
✔ Remainder: `324`
➡️ Answer in fractional form:
> `3k + 37 + 324/(k - 9)`

---

2) Divide: `(-3y² + 6) ÷ (y - 4)`

Note: The dividend is `-3y² + 0y + 6`.

```
-3y - 12
_______________
y - 4 ) -3y² + 0y + 6
-3y² + 12y
----------
-12y + 6
-12y + 48
---------
-42
```

✔ Quotient: `-3y - 12`
✔ Remainder: `-42`
➡️ Answer in fractional form:
> `-3y - 12 - 42/(y - 4)`

*(Note: We write the negative remainder as subtracting a positive fraction.)*

---

3) Divide: `(z² - 19z - 11) ÷ (z + 8)`

```
z - 27
_______________
z + 8 ) z² - 19z - 11
z² + 8z
--------
-27z - 11
-27z - 216
-----------
205
```

✔ Quotient: `z - 27`
✔ Remainder: `205`
➡️ Answer in fractional form:
> `z - 27 + 205/(z + 8)`

---

4) Divide: `(-b² + 16b² - 13b + 5) ÷ (b + 4)`

⚠️ Wait — the dividend says `-b² + 16b²`, which simplifies to `15b²`. Probably a typo? But let’s assume it’s written correctly:
→ Dividend: `-b² + 16b² - 13b + 5 = 15b² - 13b + 5`

Now divide `(15b² - 13b + 5) ÷ (b + 4)`

```
15b - 73
_______________
b + 4 ) 15b² - 13b + 5
15b² + 60b
----------
-73b + 5
-73b - 292
---------
297
```

✔ Quotient: `15b - 73`
✔ Remainder: `297`
➡️ Answer in fractional form:
> `15b - 73 + 297/(b + 4)`

---

5) Divide: `(2h² + 13h² - 14h + 4) ÷ (h + 3)`

Again, check the dividend: `2h² + 13h² = 15h²` → So dividend is `15h² - 14h + 4`

Divide `(15h² - 14h + 4) ÷ (h + 3)`

```
15h - 59
_______________
h + 3 ) 15h² - 14h + 4
15h² + 45h
----------
-59h + 4
-59h - 177
---------
181
```

✔ Quotient: `15h - 59`
✔ Remainder: `181`
➡️ Answer in fractional form:
> `15h - 59 + 181/(h + 3)`

---

6) Divide: `(z² - 19z - 11) ÷ (z + 8)`

Wait — this is identical to problem #3!
Same dividend and divisor.

So we already solved it:

✔ Quotient: `z - 27`
✔ Remainder: `205`
➡️ Answer in fractional form:
> `z - 27 + 205/(z + 8)`

---

## ✔ Final Answers (in fractional form):

1) `3k + 37 + 324/(k - 9)`
2) `-3y - 12 - 42/(y - 4)`
3) `z - 27 + 205/(z + 8)`
4) `15b - 73 + 297/(b + 4)`
5) `15h - 59 + 181/(h + 3)`
6) `z - 27 + 205/(z + 8)`

---

📌 Note on Problems 4 & 5: The dividends had redundant terms (`-b² + 16b²`, `2h² + 13h²`). I simplified them assuming they were meant to be combined. If you meant something else (e.g., a typo), please clarify!

Let me know if you’d like step-by-step work shown for any specific problem!