complete the table by identifying the degree and number of terms for each polynomial:

\begin{tabular}{|c|c|c|}
\hline
\text{polynomial} & \text{degree} & \text{number of terms} \\
\hline
x^5 + 5x^3 - 2x^2 + 3x & & \\
\hline
5 - t - 2t^2 & & \\
\hline
8y - \frac{6y^2}{y} & & \\
\hline
2xy^3 + 3 & & \\
\hline
4m - m^2 + 1 & & \\
\hline
-2g^3h & & \\
\hline
\end{tabular}

Question

complete the table by identifying the degree and number of terms for each polynomial:

\begin{tabular}{|c|c|c|}
\hline
\text{polynomial} & \text{degree} & \text{number of terms} \\
\hline
x^5 + 5x^3 - 2x^2 + 3x & & \\
\hline
5 - t - 2t^2 & & \\
\hline
8y - \frac{6y^2}{y} & & \\
\hline
2xy^3 + 3 & & \\
\hline
4m - m^2 + 1 & & \\
\hline
-2g^3h & & \\
\hline
\end{tabular}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Degree", "Polynomial Terms" ], "new_concepts": [], "current_concepts": [ "Polynomial Degree", "Polynomial Terms" ] } ## Simplify and analyze each expression $$ \begin{aligned} &\text{Row 1: } x^4 + 5x^3 - 2x^2 + 3x \implies \text{Degree: } 4 \text{ (quartic)}, \text{ Terms: } 4 \text{ (four terms)} \ &\text{Row 2: } 5 - t - 2t^2 \implies \text{Degree: } 2 \text{ (quadratic)}, \text{ Terms: } 3 \text{ (trinomial)} \ &\text{Row 3: } 8y - \frac{6y^3}{y} = 8y - 6y^2 \implies \text{Degree: } 2 \text{ (quadratic)}, \text{ Terms: } 2 \text{ (binomial)} \ &\text{Row 4: } 2x^2y^3 + 3 \implies \text{Degree: } 2+3=5 \text{ (quintic)}, \text{ Terms: } 2 \text{ (binomial)} \ &\text{Row 5: } 4m - m^3 + 1 \implies \text{Degree: } 3 \text{ (cubic)}, \text{ Terms: } 3 \text{ (trinomial)} \ &\text{Row 6: } -2g^3h \implies \text{Degree: } 3+1=4 \text{ (quartic)}, \text{ Terms: } 1 \text{ (monomial)} \end{aligned} $$ ## Match with the given drag-and-drop options $$ \begin{aligned} &\text{Options available at the bottom: } \ &\text{"binomial", "trinomial", "monomial", "4th degree", "four terms", "quintic", "cubic", "quartic", "quadratic"} \ &\text{Row 1: Degree = quartic, Number of Terms = four terms} \ &\text{Row 2: Degree = quadratic, Number of Terms = trinomial} \ &\text{Row 3: Degree = quadratic, Number of Terms = binomial} \ &\text{Row 4: Degree = quintic, Number of Terms = binomial} \ &\text{Row 5: Degree = cubic, Number of Terms = trinomial} \ &\text{Row 6: Degree = quartic, Number of Terms = monomial} \end{aligned} $$ | Polynomial | Degree | Number of Terms | |---|---|---| | $x^4+5x^3-2x^2+3x$ | quartic | four terms | | $5-t-2t^2$ | quadratic | trinomial | | $8y-\frac{6y^3}{y}$ | quadratic | binomial | | $2x^2y^3+3$ | quintic | binomial | | $4m-m^3+1$ | cubic | trinomial | | $-2g^3h$ | quartic | monomial | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Degree" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Simplify and analyze each expression

Match with the given drag-and-drop options

Answer:

Polynomial	Degree	Number of Terms
\(5-t-2t^2\)	quadratic	trinomial
\(8y-\frac{6y^3}{y}\)	quadratic	binomial
\(2x^2y^3+3\)	quintic	binomial
\(4m-m^3+1\)	cubic	trinomial
\(-2g^3h\)	quartic	monomial