Question

question 5 of 16, step 1 of 1

completely factor the trinomial, if possible.

\\x^2 + 3x + 55\\

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not factorable

Explanation:

Identify the trinomial to factor

Using the Factoring Trinomials knowledge point
We are given the trinomial:

$$ x^2 + 3x + 55 $$

This is a quadratic trinomial of the form \(ax^2 + bx + c\) where \(a = 1\), \(b = 3\), and \(c = 55\).

Find factors with given sum and product

Using the Finding Factors with Given Sum and Product knowledge point
We need to find two integers whose product is \(c = 55\) and whose sum is \(b = 3\).

Let's list the integer factor pairs of \(55\) and calculate their sums:

• \(1 \times 55 = 55\), sum: \(1 + 55 = 56\)
• \((-1) \times (-55) = 55\), sum: \(-1 - 55 = -56\)
• \(5 \times 11 = 55\), sum: \(5 + 11 = 16\)
• \((-5) \times (-11) = 55\), sum: \(-5 - 11 = -16\)

Determine factorability

No integer factor pairs of \(55\) add up to \(3\). Since there are no such integers, the trinomial cannot be factored over the integers. Therefore, the trinomial is prime (not factorable).

Answer:

• Not Factorable