select all the correct answers.

which statements are true about the result of simplifying this polynomial?
\t^3(8 + 9t) - (t^2 + 4)(t^2 - 3t)\

- the simplified expression is a polynomial.
- the simplified expression is cubic.
- the simplified expression is a trinomial.
- the simplified expression has a constant term.
- the simplified expression has four terms.

Question

select all the correct answers.

which statements are true about the result of simplifying this polynomial?
\t^3(8 + 9t) - (t^2 + 4)(t^2 - 3t)\

- the simplified expression is a polynomial.
- the simplified expression is cubic.
- the simplified expression is a trinomial.
- the simplified expression has a constant term.
- the simplified expression has four terms.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Classification", "Degree of Polynomials" ], "new_concepts": [], "current_concepts": [ "Polynomial Classification", "Degree of Polynomials", "Polynomial Addition", "Combining Like Terms" ] } ## Expand the terms of the expression $$ \begin{aligned} t^3(8 + 9t) &= 8t^3 + 9t^4 \ (t^2 + 4)(t^2 - 3t) &= t^4 - 3t^3 + 4t^2 - 12t \end{aligned} $$ ## Subtract the expanded parts and combine like terms $$ \begin{aligned} (8t^3 + 9t^4) - (t^4 - 3t^3 + 4t^2 - 12t) &= 9t^4 + 8t^3 - t^4 + 3t^3 - 4t^2 + 12t \ &= 8t^4 + 11t^3 - 4t^2 + 12t \end{aligned} $$ ## Analyze the properties of the simplified expression $$ \begin{aligned} &\text{Expression: } 8t^4 + 11t^3 - 4t^2 + 12t \ &\text{Type: Polynomial (True)} \ &\text{Degree: 4 (Quartic, not cubic) (False)} \ &\text{Number of terms: 4 (not a trinomial) (True)} \ &\text{Constant term: 0 (no non-zero constant term) (False)} \end{aligned} $$

The simplified expression is a polynomial.

The simplified expression is cubic.

The simplified expression is a trinomial.

The simplified expression has a constant term.

The simplified expression has four terms.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Classification" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the terms of the expression

Subtract the expanded parts and combine like terms

Analyze the properties of the simplified expression

Answer: