Questions: Factor the trinomial. a^2-3a+19

Factor the trinomial. a^2-3a+19
Transcript text: Factor the trinomial. \[ a^{2}-3 a+19 \]
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Solution

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Solution Steps

Step 1: Identify the trinomial

The given trinomial is \( a^{2} - 3a + 19 \).

Step 2: Check for factorability

To determine if the trinomial is factorable, we check if there exist two numbers \( m \) and \( n \) such that:

  1. \( m \cdot n = 19 \) (the constant term).
  2. \( m + n = -3 \) (the coefficient of the middle term).
Step 3: Test possible pairs

The pairs of factors of 19 are:

  • \( (1, 19) \): \( 1 + 19 = 20 \neq -3 \).
  • \( (-1, -19) \): \( -1 + (-19) = -20 \neq -3 \).

Since no pair of factors satisfies both conditions, the trinomial is not factorable.

Step 4: Select the correct choice

The correct choice is: B. The trinomial is not factorable.

Final Answer

The correct answer is B. The trinomial is not factorable.

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