type the correct answer in each box. use numerals instead of words.

simplify the following polynomial expression.

\(5x^2 + 13x - 4) - (17x^2 + 7x - 19) + (5x - 7)(3x + 1)\

\\box x^2 - \box x + \box\

Question

type the correct answer in each box. use numerals instead of words.

simplify the following polynomial expression.

\(5x^2 + 13x - 4) - (17x^2 + 7x - 19) + (5x - 7)(3x + 1)\

\\box x^2 - \box x + \box\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Subtraction", "Multiplying Binomials", "Combining Like Terms", "Polynomial Simplification" ], "new_concepts": [], "current_concepts": [ "Polynomial Subtraction", "Multiplying Binomials", "Combining Like Terms", "Polynomial Simplification" ] } ## Multiply the binomials $$ (5x - 7)(3x + 1) = 15x^2 + 5x - 21x - 7 = 15x^2 - 16x - 7 $$ ## Distribute the negative sign and rewrite the expression $$ (5x^2 + 13x - 4) - 17x^2 - 7x + 19 + 15x^2 - 16x - 7 $$ ## Combine like terms $$ \begin{aligned} x^2\text{ terms: } & 5x^2 - 17x^2 + 15x^2 = 3x^2 \ x\text{ terms: } & 13x - 7x - 16x = -10x \ \text{Constant terms: } & -4 + 19 - 7 = 8 \ \text{Result: } & 3x^2 - 10x + 8 \end{aligned} $$ Simplify the following polynomial expression. $$(5x^2 + 13x - 4) - (17x^2 + 7x - 19) + (5x - 7)(3x + 1)$$ 3 $x^2$ $-$ 10 $x$ $+$ 8 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Simplification" ] }

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QUESTION IMAGE

Question

Explanation:

Multiply the binomials

Distribute the negative sign and rewrite the expression

Combine like terms

Answer: