which expressions are perfect square trinomials? check all that apply.

$x^2 + 16x + 8$
$x^2 + 14x + 49$
$x^2 - 5x + 25$
$x^2 - 24x + 144$
$x^2 + 9x - 81$

Question

which expressions are perfect square trinomials? check all that apply.

$x^2 + 16x + 8$
  $x^2 + 14x + 49$
  $x^2 - 5x + 25$
  $x^2 - 24x + 144$
  $x^2 + 9x - 81$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perfect Square Trinomial" ], "new_concepts": [], "current_concepts": [ "Perfect Square Trinomial", "Factoring Polynomials" ] } ## Define perfect square trinomial criteria $$ (x \pm a)^2 = x^2 \pm 2ax + a^2 $$ ## Test each given expression $$ \begin{aligned} &\text{For } x^2 + 16x + 8: \quad a^2 = 8 \implies a = \sqrt{8}, \quad 2a = 4\sqrt{2} e 16 \quad (\text{Incorrect})\ &\text{For } x^2 + 14x + 49: \quad a^2 = 49 \implies a = 7, \quad 2a = 14 \quad (\text{Correct})\ &\text{For } x^2 - 5x + 25: \quad a^2 = 25 \implies a = 5, \quad 2a = 10 e 5 \quad (\text{Incorrect})\ &\text{For } x^2 - 24x + 144: \quad a^2 = 144 \implies a = 12, \quad 2a = 24 \quad (\text{Correct})\ &\text{For } x^2 + 9x - 81: \quad a^2 = -81 \quad (\text{Incorrect, constant must be positive}) \end{aligned} $$ ## Identify correct options $$ \begin{aligned} &x^2 + 14x + 49 = (x + 7)^2\ &x^2 - 24x + 144 = (x - 12)^2 \end{aligned} $$

$x^2 + 16x + 8$

$x^2 + 14x + 49$

$x^2 - 5x + 25$

$x^2 - 24x + 144$

$x^2 + 9x - 81$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Perfect Square Trinomial" ] }

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QUESTION IMAGE

Question

Explanation:

Define perfect square trinomial criteria

Test each given expression

Identify correct options

Answer: