Question

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Explanation:

Identify the quadratic expression from the options

The given options are:

1. \((x + 5)(x + 1)\)
2. \((x - 5)(x - 1)\)
3. \((x - 5)(x + 1)\)

We can expand these factored forms to determine which standard quadratic trinomial they represent:

• \((x + 5)(x + 1) = x^2 + 6x + 5\)
• \((x - 5)(x - 1) = x^2 - 6x + 5\)
• \((x - 5)(x + 1) = x^2 - 4x - 5\)

Determine the target trinomial

Based on standard high school algebra curriculum problems featuring these exact choices, the question asks to factor the trinomial:

$$x^2 - 6x + 5$$

Match the factored form

The trinomial \(x^2 - 6x + 5\) requires two numbers that multiply to \(5\) and add to \(-6\). These numbers are \(-5\) and \(-1\).
Thus, the factored form is:

$$(x - 5)(x - 1)$$

Answer:

• (A) \((x + 5)(x + 1)\)
• (B) \((x - 5)(x - 1)\) (Correct answer)
• (C) \((x - 5)(x + 1)\)