finding the factors of a trinomial

what are the factors of $x^2 - 4x - 5$? check all that apply.

$x - 5$
$x - 2$
$x - 1$
$x + 1$
$x + 2$
$x + 5$

Question

finding the factors of a trinomial

what are the factors of $x^2 - 4x - 5$? check all that apply.

$x - 5$
  $x - 2$
  $x - 1$
  $x + 1$
  $x + 2$
  $x + 5$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Factoring Trinomials" ], "current_concepts": [ "Factoring Trinomials", "Algebra Tiles" ] } ## Identify the trinomial to factor The given trinomial is: $$ x^2 - 4x - 5 $$ ## Find two numbers that multiply to $ac$ and add to $b$ For the quadratic expression $ax^2 + bx + c$, we have $a = 1$, $b = -4$, and $c = -5$. We need two integers whose product is $a \cdot c = -5$ and whose sum is $b = -4$. The factors of $-5$ are: $$ \begin{aligned} &(-5) \cdot 1 = -5 \quad \text{and} \quad -5 + 1 = -4\ &5 \cdot (-1) = -5 \quad \text{and} \quad 5 + (-1) = 4 \end{aligned} $$ The correct pair is $-5$ and $1$. ## Write the factored form Using the found integers, we write the trinomial in its factored form: $$ x^2 - 4x - 5 = (x - 5)(x + 1) $$ Thus, the factors are $x - 5$ and $x + 1$.

(A) $x - 5$

(B) $x - 2$

(C) $x - 1$

(D) $x + 1$

(E) $x + 2$

(F) $x + 5$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Factoring Trinomials" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the trinomial to factor

Find two numbers that multiply to \(ac\) and add to \(b\)

Write the factored form

Answer: