Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
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.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.