The first step in the process for factoring the trinomial [tex]x^2-4 x-32[/tex] is to:
A. find the sum of the factors of 32
B. list all the factors of 32
C. list all the factors of the 4
D. find the sum of the factors of 4
Answer (1)
List the factors of the constant term (32) to find potential pairs that multiply to -32.
Consider both positive and negative factors.
Find a pair of factors that add up to the coefficient of the linear term (-4).
The first step is to list all the factors of 32: list all the factors of 32 .
Explanation
Understanding the Problem We are given the trinomial x 2 − 4 x − 32 and asked to identify the first step in factoring it. Factoring a trinomial of the form x 2 + b x + c involves finding two numbers that multiply to c and add up to b . In this case, we need to find two numbers that multiply to -32 and add up to -4.
Identifying the First Step To factor the trinomial x 2 − 4 x − 32 , we need to find two numbers that multiply to -32 and add up to -4. The first step in this process is to list the factors of 32 (or -32) to find potential candidates.
Listing Factors of 32 The factors of 32 are: 1, 2, 4, 8, 16, and 32. We need to consider both positive and negative factors to find a pair that multiplies to -32 and adds to -4.
Conclusion Therefore, the first step in factoring the trinomial x 2 − 4 x − 32 is to list all the factors of 32.
Examples
Factoring trinomials is a fundamental skill in algebra and has practical applications in various fields. For example, engineers use factoring to simplify complex equations when designing structures or analyzing systems. Architects use factoring to determine dimensions and optimize space in building designs. Understanding factoring helps in solving real-world problems involving quadratic relationships.
