Question

what is the initial step when factoring a trinomial of the form $ax^2 + bx + c$ where $a$ is not equal to 1, using the conceptual method? find two factors of b that sum to ac; split the middle term into two terms; multiply a and c; identify the greatest common factor (gcf) of all terms

Explanation:

When factoring a trinomial \( ax^{2}+bx + c \) (\( a
eq1 \)) using the conceptual (or "ac - method"): The first step is to identify the greatest common factor (GCF) of all three terms (\( ax^{2} \), \( bx \), \( c \)). If there is a GCF, we factor it out first. For example, in \( 2x^{2}+4x + 2 \), the GCF of \( 2x^{2} \), \( 4x \), and \( 2 \) is \( 2 \), so we factor that out first to get \( 2(x^{2}+2x + 1) \). The other options: multiplying \( a \) and \( c \) is part of the "ac - method" but not the initial step (the initial step is checking for GCF), finding factors of \( b \) that sum to \( ac \) is later in the "ac - method", and splitting the middle term comes after finding those factors. So the initial step is identifying the GCF of all terms.

Answer:

D. Identify the greatest common factor (GCF) of all terms