the polynomial $8x^2 - 8x + 2 - 5 + x$ is simplified to $8x^2 - gx - h$. what are the value of $g$ and $h$?

$g = -9$ and $h = 7$

$g = 9$ and $h = -3$

$g = -7$ and $h = 7$

$g = 7$ and $h = 3$

Question

the polynomial $8x^2 - 8x + 2 - 5 + x$ is simplified to $8x^2 - gx - h$. what are the value of $g$ and $h$?

$g = -9$ and $h = 7$

$g = 9$ and $h = -3$

$g = -7$ and $h = 7$

$g = 7$ and $h = 3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Combining Like Terms", "Standard Form of a Polynomial" ], "new_concepts": [], "current_concepts": [ "Combining Like Terms", "Standard Form of a Polynomial", "Polynomial Simplification" ] } ## Group the like terms Using the *Combining Like Terms* knowledge point $$ \begin{aligned} 8x^2 - 8x + 2 - 5 + x &= 8x^2 + (-8x + x) + (2 - 5) \end{aligned} $$ ## Simplify the coefficients Using the *Combining Like Terms* knowledge point $$ \begin{aligned} -8x + x &= -7x\ 2 - 5 &= -3 \end{aligned} $$ ## Write in standard form Using the *Standard Form of a Polynomial* knowledge point $$ \begin{aligned} 8x^2 - 7x - 3 \end{aligned} $$ ## Compare with target expression Using the *Standard Form of a Polynomial* knowledge point $$ \begin{aligned} 8x^2 - gx - h &= 8x^2 - 7x - 3\ -gx &= -7x \implies g = 7\ -h &= -3 \implies h = 3 \end{aligned} $$

$g = -9$ and $h = 7$

$g = 9$ and $h = -3$

$g = -7$ and $h = 7$

$g = 7$ and $h = 3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Combining Like Terms" ] }

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QUESTION IMAGE

Question

Explanation:

Group the like terms

Simplify the coefficients

Write in standard form

Compare with target expression

Answer: