\4x^4y^2 + 5x^2y^5 + 2 - 7xy\

a) number of terms

b) degree

c) leading coefficient

d) type of polynomial

Question

\4x^4y^2 + 5x^2y^5 + 2 - 7xy\

a) number of terms

b) degree

c) leading coefficient

d) type of polynomial

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Terms", "Polynomial Degree", "Leading Coefficient", "Polynomial Classification" ], "new_concepts": [], "current_concepts": [ "Polynomial Terms", "Polynomial Degree", "Leading Coefficient", "Polynomial Classification" ] } ## Identify the terms and count them $$ \text{Terms: } 4x^4y^2,\ 5x^2y^5,\ 2,\ -7xy $$ $$ \text{Number of terms} = 4 $$ ## Determine the degree of each term and the polynomial $$ \begin{aligned} &\text{Degree of } 4x^4y^2 = 4 + 2 = 6\ &\text{Degree of } 5x^2y^5 = 2 + 5 = 7\ &\text{Degree of } 2 = 0\ &\text{Degree of } -7xy = 1 + 1 = 2\ &\text{Polynomial Degree} = \max(6, 7, 0, 2) = 7 \end{aligned} $$ ## Identify the leading term, leading coefficient, and polynomial type $$ \begin{aligned} &\text{Leading term (highest degree)} = 5x^2y^5\ &\text{Leading Coefficient} = 5\ &\text{Type of Polynomial (by number of terms)} = \text{Polynomial (or multinomial, since it has 4 terms)} \end{aligned} $$ Given the polynomial: $$ 4x^4y^2 + 5x^2y^5 + 2 - 7xy $$ a) Number of terms: 4 b) Degree: 7 c) Leading Coefficient: 5 d) Type of Polynomial: Polynomial (or multinomial) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Classification" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the terms and count them

Determine the degree of each term and the polynomial

Identify the leading term, leading coefficient, and polynomial type

Answer: