Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
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.
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.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.