question 1 of 5

select the correct answer.

consider the polynomials given below.
$p = 11x^5 + 9x^4 - 4x^3 - 7x^2 + 5$
$q = (2x^2 + 1)(4x^2 - 3)$

determine the operation that results in the simplified expression below.
$11x^5 + x^4 - 4x^3 - 5x^2 + 8$

$p - q$
$p + q$
$pq$
$q - p$

Question

question 1 of 5

select the correct answer.

consider the polynomials given below.
$p = 11x^5 + 9x^4 - 4x^3 - 7x^2 + 5$
$q = (2x^2 + 1)(4x^2 - 3)$

determine the operation that results in the simplified expression below.
$11x^5 + x^4 - 4x^3 - 5x^2 + 8$

$p - q$
$p + q$
$pq$
$q - p$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Polynomial Operations" ], "new_concepts": [], "current_concepts": [ "Polynomial Operations", "Factoring Polynomials" ] } ## Expand the polynomial $Q$ $$ \begin{aligned} Q &= (2x^2 + 1)(4x^2 - 3) \ &= 8x^4 - 6x^2 + 4x^2 - 3 \ &= 8x^4 - 2x^2 - 3 \end{aligned} $$ ## Test the operation $P - Q$ $$ \begin{aligned} P - Q &= (11x^5 + 9x^4 - 4x^3 - 7x^2 + 5) - (8x^4 - 2x^2 - 3) \ &= 11x^5 + (9 - 8)x^4 - 4x^3 + (-7 - (-2))x^2 + (5 - (-3)) \ &= 11x^5 + x^4 - 4x^3 - 5x^2 + 8 \end{aligned} $$ ## Compare with the target expression The target expression is $11x^5 + x^4 - 4x^3 - 5x^2 + 8$, which matches $P - Q$.

(A) $P - Q$

(B) $P + Q$

(C) $PQ$

(D) $Q - P$

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

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QUESTION IMAGE

Question

Explanation:

Expand the polynomial \(Q\)

Test the operation \(P - Q\)

Compare with the target expression

Answer: