adding polynomials

to add or subtract two polynomials, we combine like terms. recall that two terms are like terms if they each have the same variables and the corresponding variables are raised to the same powers.

examples: add and simplify

$(-9x^9 - 4x^7 + 8x^4 - 3) + (8x^8 + 7x^4 - 9x) + (-3x^7 - 4x^4 - 9x + 7)$

Question

adding polynomials

to add or subtract two polynomials, we combine like terms. recall that two terms are like terms if they each have the same variables and the corresponding variables are raised to the same powers.

examples: add and simplify

$(-9x^9 - 4x^7 + 8x^4 - 3) + (8x^8 + 7x^4 - 9x) + (-3x^7 - 4x^4 - 9x + 7)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Adding Polynomials", "Combining Like Terms" ], "new_concepts": [], "current_concepts": [ "Adding Polynomials", "Combining Like Terms" ] } ## Group terms by degree $$ \begin{aligned} x^9 \text{ terms: } & -9x^9 \ x^8 \text{ terms: } & 8x^8 \ x^7 \text{ terms: } & -4x^7 - 3x^7 \ x^4 \text{ terms: } & 8x^4 + 7x^4 - 4x^4 \ x^1 \text{ terms: } & -9x - 9x \ \text{Constant terms: } & -3 + 7 \end{aligned} $$ ## Combine coefficients for each degree $$ \begin{aligned} -9x^9 & = -9x^9 \ 8x^8 & = 8x^8 \ (-4 - 3)x^7 & = -7x^7 \ (8 + 7 - 4)x^4 & = 11x^4 \ (-9 - 9)x & = -18x \ -3 + 7 & = 4 \end{aligned} $$ ## Write the simplified polynomial in descending order $$ -9x^9 + 8x^8 - 7x^7 + 11x^4 - 18x + 4 $$ Add and Simplify: $$(-9x^9 - 4x^7 + 8x^4 - 3) + (8x^8 + 7x^4 - 9x) + (-3x^7 - 4x^4 - 9x + 7) =$$ $-9x^9 + 8x^8 - 7x^7 + 11x^4 - 18x + 4$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Adding Polynomials" ] }

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QUESTION IMAGE

Question

Explanation:

Group terms by degree

Combine coefficients for each degree

Write the simplified polynomial in descending order

Answer: