To solve the problem of factoring the trinomial [tex]\( ax^2 + bx + c \)[/tex], we need to follow a systematic approach. Here's a step-by-step guide to understand the process:
1. Identify the coefficients: First, you should identify the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] in the trinomial [tex]\( ax^2 + bx + c \)[/tex].
- [tex]\( a \)[/tex] is the coefficient of [tex]\( x^2 \)[/tex],
- [tex]\( b \)[/tex] is the coefficient of [tex]\( x \)[/tex],
- [tex]\( c \)[/tex] is the constant term.
2. List the factors of the constant term [tex]\( c \)[/tex]: The first step in factoring this trinomial is to consider the factors of the constant term [tex]\( c \)[/tex]. This helps in finding pairs of factors that can add or combine to yield the necessary middle term coefficient [tex]\( b \)[/tex].
- For example, if [tex]\( c = 6 \)[/tex], the factors are [tex]\( \{1, 6\}, \{-1, -6\}, \{2, 3\}, \{-2, -3\} \)[/tex].
3. Check factor combinations: Once you have listed the factors of [tex]\( c \)[/tex], you then check which pairs of these factors can multiply to [tex]\( c \)[/tex] and add up to the coefficient [tex]\( b \)[/tex].
With these steps in mind, we can clearly see that the very first step is crucial in the factoring process:
Answer: A. List the factors of the constant term.
