Problem 18 - Algebra and Trigonometry

Question

Factor each trinomial, or state that the trinomial is prime. $$x^{2}+8 x+15$$

Step-by-Step Solution

Answer

The factored form of \(x^2+8x+15\) is \( (x + 3)(x + 5)\).

Step 1: Identify the coefficients

Begin by identifying coefficients in the trinomial. The coefficients in the equation \(x^2+8x+15\) are a=1, b=8 and c=15.

Step 2: Find the factors of c

We need to find two numbers that multiply to 15 and add up to 8. By considering the factors of 15 (1, 3, 5, 15), it's easy to see that the numbers 3 and 5 fit the criteria as they multiply to give 15 and add to give 8.

Step 3: Write the factored form

Using the two numbers found, write the factors of the trinomial in the form \( (x + n)(x + m)\), where n and m are the numbers found in Step 2. So the factored form of \(x^2+8x+15\) is \( (x + 3)(x + 5)\).