Printable worksheet from Quizizz featuring 10 questions on polynomial operations, including addition, subtraction, and simplification, with multiple-choice answers.

Let’s solve each problem one by one.

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Problem 1: Find the sum.
(2x² + 5x - 7) + (3 - 4x² + 6x)

Step 1: Remove parentheses — since it’s addition, signs stay the same.
→ 2x² + 5x - 7 + 3 - 4x² + 6x

Step 2: Group like terms.
x² terms: 2x² - 4x² = -2x²
x terms: 5x + 6x = 11x
constants: -7 + 3 = -4

Final: -2x² + 11x - 4 → That’s option A

✔ Verified.

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Problem 2: Find the sum.
(3y² + y³ - 5) + (4y² - 4y + 2y³ + 8)

Step 1: Remove parentheses.
→ 3y² + y³ - 5 + 4y² - 4y + 2y³ + 8

Step 2: Group like terms.
y³ terms: y³ + 2y³ = 3y³
y² terms: 3y² + 4y² = 7y²
y terms: -4y
constants: -5 + 8 = 3

Final: 3y³ + 7y² - 4y + 3 → That’s option B

✔ Verified.

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Problem 3: Find the difference.
(3 - 2x + 2x²) - (4x - 5 + 3x²)

Step 1: Distribute the negative sign to the second polynomial.
→ 3 - 2x + 2x² - 4x + 5 - 3x²

Step 2: Group like terms.
x² terms: 2x² - 3x² = -x²
x terms: -2x - 4x = -6x
constants: 3 + 5 = 8

Final: -x² - 6x + 8 → That’s option A

✔ Verified.

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Problem 4: Simplify the expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

Step 1: Distribute the negative sign.
→ 4n⁴ - 8n + 4 - 8n² - 4n⁴ - 1

Step 2: Group like terms.
n⁴ terms: 4n⁴ - 4n⁴ = 0
n² terms: -8n²
n terms: -8n
constants: 4 - 1 = 3

Final: -8n² - 8n + 3 → That’s option D

✔ Verified.

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Problem 5: Simplify each expression.
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

Step 1: Rewrite in standard order (optional but helpful):
First polynomial: -b⁴ + 6b³ + 6
Second polynomial: 8b³ - 6b⁴ + 2 → rewrite as -6b⁴ + 8b³ + 2

But better to just distribute negative directly:

→ 6b³ + 6 - b⁴ - 8b³ + 6b⁴ - 2

Step 2: Group like terms.
b⁴ terms: -b⁴ + 6b⁴ = 5b⁴
b³ terms: 6b³ - 8b³ = -2b³
constants: 6 - 2 = 4

Final: 5b⁴ - 2b³ + 4 → That’s option A

✔ Verified.

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Problem 6: Simplify each expression.
(6x + 4x⁴ - 3x²) + (7x⁴ + 5x² + 8x)

Step 1: Remove parentheses (addition, so no sign changes).
→ 6x + 4x⁴ - 3x² + 7x⁴ + 5x² + 8x

Step 2: Group like terms.
x⁴ terms: 4x⁴ + 7x⁴ = 11x⁴
x² terms: -3x² + 5x² = 2x²
x terms: 6x + 8x = 14x

Final: 11x⁴ + 2x² + 14x

Wait — this doesn’t match any of the visible options? Let me check the image again.

Looking back at the user’s image, Problem 6 is cut off — we don’t see the answer choices for #6. But since the instruction says “solve the problem accurately” and only problems 1–5 have full answer choices shown, and the user didn’t specify which problem to solve, I’ll assume they want all solved up to where options are visible.

Actually, re-reading the prompt: “Solve the problem accurately.” — plural? But the image has 10 questions, though only 6 are visible. Since the user didn’t specify which one, and the first 5 are complete with options, I’ll provide answers for 1–5.

But wait — the final answer section should contain the correct choice for each? Or just one? The format says “Final Answer: [Provide only the final correct answer]” — singular.

Hmm. Looking at the structure, perhaps the user expects us to pick one problem? But the image shows multiple.

Actually, rereading the initial instruction: “You are an educational assistant helping a student solve homework problems.” — and the image contains a quiz with 10 questions. But the user didn’t specify which one.

However, in such cases, typically we solve all that are fully presented. But the response format says “Final Answer:” — implying one answer.

This is ambiguous. But looking at the way the question is phrased — “the problem” — singular — maybe they mean the entire set? But that doesn’t fit.

Alternatively, perhaps the user intended to upload one problem but uploaded a whole page. Given the constraints, and since Problems 1–5 are complete with options, and Problem 6 is cut off, I’ll provide the answers for 1–5 as a list.

But the format requires “Final Answer:” — so perhaps I should list them.

Wait — the instruction says: “If you're solving math or logic problems, verify your answer before writing it in the Final Answer section.” — and “Final Answer: [Provide only the final correct answer]”

Perhaps for multiple choice, we list the letters.

Given that, and to be safe, I’ll provide the correct choices for Problems 1 through 5.

But let me double-check Problem 6 even though options aren't visible — maybe I can still simplify it.

Problem 6: (6x + 4x⁴ - 3x²) + (7x⁴ + 5x² + 8x)

As above: 4x⁴ + 7x⁴ = 11x⁴
-3x² + 5x² = 2x²
6x + 8x = 14x
So: 11x⁴ + 2x² + 14x

Since no options are visible, I won’t include it in final answer.

Now, for the final answer, since the user might expect one answer, but there are five problems, I think the best approach is to list the correct choices for each problem that was fully presented.

But the format says “Final Answer:” — singular. Perhaps I should output the answers as a sequence.

Looking at similar tasks, sometimes they expect the answer to the first problem, but that seems arbitrary.

Another idea: perhaps the user wants me to solve all, and the final answer is the set.

I think I’ll go with listing the correct options for Problems 1 to 5.

So:

Problem 1: A
Problem 2: B
Problem 3: A
Problem 4: D
Problem 5: A

But how to format that in "Final Answer"?

Perhaps: A, B, A, D, A

Yes, that makes sense.

Let me confirm once more:

1. A ✓
2. B ✓
3. A ✓
4. D ✓
5. A ✓

All verified.

Final Answer: A, B, A, D, A