Long Division Worksheets - Practice Questions and Answers | Cazoomy - Free Printable

It looks like you've uploaded a Polynomial Long Division Worksheet, and the task is to divide each polynomial using long division and write the remainder in fractional form.

Let’s go through each problem one by one. I'll solve them step-by-step, showing the long division process and then express the remainder as a fraction.

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🔷 Problem 1:

$$
\frac{3k^2 + 10k - 9}{k - 9}
$$

We perform polynomial long division:

1. Divide $3k^2 \div k = 3k$
2. Multiply: $3k(k - 9) = 3k^2 - 27k$
3. Subtract: $(3k^2 + 10k) - (3k^2 - 27k) = 37k$
4. Bring down $-9$: now we have $37k - 9$
5. Divide $37k \div k = 37$
6. Multiply: $37(k - 9) = 37k - 333$
7. Subtract: $(37k - 9) - (37k - 333) = 324$

So:
$$
\frac{3k^2 + 10k - 9}{k - 9} = 3k + 37 + \frac{324}{k - 9}
$$

✔ Answer: $3k + 37 + \frac{324}{k - 9}$

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🔷 Problem 2:

$$
\frac{-3y^2 + 6}{y - 4}
$$

Note: The dividend is $-3y^2 + 0y + 6$, so we include the missing $y$ term.

1. Divide $-3y^2 \div y = -3y$
2. Multiply: $-3y(y - 4) = -3y^2 + 12y$
3. Subtract: $(-3y^2 + 0y) - (-3y^2 + 12y) = -12y$
4. Bring down $+6$: now $-12y + 6$
5. Divide $-12y \div y = -12$
6. Multiply: $-12(y - 4) = -12y + 48$
7. Subtract: $(-12y + 6) - (-12y + 48) = -42$

So:
$$
\frac{-3y^2 + 6}{y - 4} = -3y - 12 + \frac{-42}{y - 4}
$$

✔ Answer: $-3y - 12 - \frac{42}{y - 4}$

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🔷 Problem 3:

$$
\frac{z^2 - 19z - 11}{z + 8}
$$

1. Divide $z^2 \div z = z$
2. Multiply: $z(z + 8) = z^2 + 8z$
3. Subtract: $(z^2 - 19z) - (z^2 + 8z) = -27z$
4. Bring down $-11$: $-27z - 11$
5. Divide $-27z \div z = -27$
6. Multiply: $-27(z + 8) = -27z - 216$
7. Subtract: $(-27z - 11) - (-27z - 216) = 205$

So:
$$
\frac{z^2 - 19z - 11}{z + 8} = z - 27 + \frac{205}{z + 8}
$$

✔ Answer: $z - 27 + \frac{205}{z + 8}$

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🔷 Problem 4:

$$
\frac{-b^2 + 16b^2 - 13b + 5}{b + 4}
$$

Wait — there's an error here: $-b^2 + 16b^2 = 15b^2$, so the dividend is:

$$
15b^2 - 13b + 5
$$

Now divide:
$$
\frac{15b^2 - 13b + 5}{b + 4}
$$

1. $15b^2 \div b = 15b$
2. Multiply: $15b(b + 4) = 15b^2 + 60b$
3. Subtract: $(15b^2 - 13b) - (15b^2 + 60b) = -73b$
4. Bring down $+5$: $-73b + 5$
5. $-73b \div b = -73$
6. Multiply: $-73(b + 4) = -73b - 292$
7. Subtract: $(-73b + 5) - (-73b - 292) = 297$

So:
$$
\frac{15b^2 - 13b + 5}{b + 4} = 15b - 73 + \frac{297}{b + 4}
$$

✔ Answer: $15b - 73 + \frac{297}{b + 4}$

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🔷 Problem 5:

$$
\frac{2h^2 + 13h^2 - 14h + 4}{h + 3}
$$

Wait — again, combine like terms: $2h^2 + 13h^2 = 15h^2$

So dividend is: $15h^2 - 14h + 4$

Now divide:
$$
\frac{15h^2 - 14h + 4}{h + 3}
$$

1. $15h^2 \div h = 15h$
2. Multiply: $15h(h + 3) = 15h^2 + 45h$
3. Subtract: $(15h^2 - 14h) - (15h^2 + 45h) = -59h$
4. Bring down $+4$: $-59h + 4$
5. $-59h \div h = -59$
6. Multiply: $-59(h + 3) = -59h - 177$
7. Subtract: $(-59h + 4) - (-59h - 177) = 181$

So:
$$
\frac{15h^2 - 14h + 4}{h + 3} = 15h - 59 + \frac{181}{h + 3}
$$

✔ Answer: $15h - 59 + \frac{181}{h + 3}$

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🔷 Problem 6:

$$
\frac{z^2 - 19z - 11}{z + 8}
$$

This is identical to Problem 3!

So same result:

$$
\frac{z^2 - 19z - 11}{z + 8} = z - 27 + \frac{205}{z + 8}
$$

✔ Answer: $z - 27 + \frac{205}{z + 8}$

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## ✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | $3k + 37 + \frac{324}{k - 9}$ |
| 2) | $-3y - 12 - \frac{42}{y - 4}$ |
| 3) | $z - 27 + \frac{205}{z + 8}$ |
| 4) | $15b - 73 + \frac{297}{b + 4}$ |
| 5) | $15h - 59 + \frac{181}{h + 3}$ |
| 6) | $z - 27 + \frac{205}{z + 8}$ |

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💡 Note: Problems 3 and 6 are identical — likely a copy-paste error on the worksheet.

Let me know if you'd like these answers formatted for printing or if you want visual step-by-step long division diagrams!