5. simplify the following polynomials.
a) $(3x^2 + 6x - 8) + (-5x^2 - x + 4)$
b) $(-6x^2 + 5x + 1) - (4x^2 + 5 - 2x)$

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Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Addition", "Polynomial Subtraction" ], "new_concepts": [], "current_concepts": [ "Polynomial Addition", "Polynomial Subtraction" ] } ## Simplify part a $$ \begin{aligned} (3x^2 + 6x - 8) + (-5x^2 - x + 4) &= 3x^2 - 5x^2 + 6x - x - 8 + 4 \ &= -2x^2 + 5x - 4 \end{aligned} $$ ## Simplify part b $$ \begin{aligned} (-6x^2 + 5x + 1) - (4x^2 + 5 - 2x) &= -6x^2 + 5x + 1 - 4x^2 - 5 + 2x \ &= -6x^2 - 4x^2 + 5x + 2x + 1 - 5 \ &= -10x^2 + 7x - 4 \end{aligned} $$ ## Question 5a $-2x^2 + 5x - 4$ ## Question 5b $-10x^2 + 7x - 4$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Addition and Subtraction" ] }

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Explanation:

Simplify part a

Simplify part b

Answer:

Question 5a

Question 5b