a, b, and c are polynomials, where $a = n$, $b = 2n + 6$, and $c = n^2 - 1$. what is $ab - c$ in simplest form?

$-n^2 + 3n + 5$
$n^2 + 6n + 1$
$2n^2 + 6n - 1$
$3n^2 + 5$

Question

a, b, and c are polynomials, where $a = n$, $b = 2n + 6$, and $c = n^2 - 1$. what is $ab - c$ in simplest form?

$-n^2 + 3n + 5$
$n^2 + 6n + 1$
$2n^2 + 6n - 1$
$3n^2 + 5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Multiplication", "Polynomial Subtraction", "Polynomial Operations" ], "new_concepts": [], "current_concepts": [ "Polynomial Multiplication", "Polynomial Subtraction", "Polynomial Operations" ] } ## Substitute the given polynomials into the expression $$ \begin{aligned} A &= n \ B &= 2n + 6 \ C &= n^2 - 1 \ AB - C &= (n)(2n + 6) - (n^2 - 1) \end{aligned} $$ ## Expand the product of polynomials $$ \begin{aligned} (n)(2n + 6) &= 2n^2 + 6n \end{aligned} $$ ## Subtract the polynomial and combine like terms $$ \begin{aligned} AB - C &= (2n^2 + 6n) - (n^2 - 1) \ &= 2n^2 + 6n - n^2 + 1 \ &= n^2 + 6n + 1 \end{aligned} $$

(A) $-n^2 + 3n + 5$

(B) $n^2 + 6n + 1$

(C) $2n^2 + 6n - 1$

(D) $3n^2 + 5$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Polynomial Operations" ] }

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QUESTION IMAGE

Question

Explanation:

Substitute the given polynomials into the expression

Expand the product of polynomials

Subtract the polynomial and combine like terms

Answer: