Questions: Factor the trinomial completely. x^2+11x+5

Factor the trinomial completely. x^2+11x+5
Transcript text: Factor the trinomial completely. \[ x^{2}+11 x+5 \]
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Solution

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Solution Steps

Step 1: Identify the Trinomial

We start with the trinomial \( x^2 + 11x + 5 \).

Step 2: Attempt to Factor

To factor the trinomial, we need to find two numbers that multiply to the constant term \( 5 \) and add to the coefficient of the linear term \( 11 \).

Step 3: Analyze the Factors

The factors of \( 5 \) are \( 1 \) and \( 5 \). However, these do not add up to \( 11 \). Therefore, the trinomial cannot be factored into rational numbers.

Step 4: Conclusion

Since the trinomial \( x^2 + 11x + 5 \) does not factor into simpler binomials with rational coefficients, it remains in its original form.

Final Answer

The trinomial cannot be factored further, so the answer is \\(\boxed{x^2 + 11x + 5}\\).

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