In factoring a trinomial with a leading coefficient other than 1, the first step is to look for a common factor in each term and factor it out.
A. True
B. False
Answer (2)
Check for a common factor in each term of the trinomial.
If a common factor exists, factor it out to simplify the trinomial.
If no common factor exists, proceed with other factoring methods.
The statement is true: the first step is to look for and factor out a common factor. T r u e
Explanation
Understanding the Problem The question asks whether the first step in factoring a trinomial with a leading coefficient other than 1 is to look for a common factor in each term and factor it out.
Checking for Common Factors Let's consider a trinomial like 2 x 2 + 4 x + 6 . The first step in factoring this trinomial would be to look for a common factor. In this case, the greatest common factor (GCF) of the terms 2 x 2 , 4 x , and 6 is 2 . Factoring out the 2 gives 2 ( x 2 + 2 x + 3 ) .
When There's No Common Factor Now, let's consider another trinomial like 3 x 2 + 5 x + 2 . In this case, there is no common factor among the terms 3 x 2 , 5 x , and 2 . So, we would proceed with other factoring methods such as the AC method or trial and error.
Conclusion Therefore, the first step in factoring a trinomial with a leading coefficient other than 1 is indeed to look for a common factor in each term and factor it out if one exists.
Examples
Factoring trinomials is used in many real-world applications, such as optimizing the design of structures, solving problems in physics, and modeling financial markets. For example, engineers use factoring to determine the dimensions of a rectangular structure given its area, which is expressed as a trinomial. By factoring the trinomial, they can find the possible lengths and widths of the structure, ensuring it meets the required specifications.
The statement is true; the first step in factoring a trinomial with a leading coefficient other than 1 is to look for and factor out any common factors from the terms. If a common factor is found, you simplify the trinomial before attempting further factoring methods. If no common factor exists, you can directly use other strategies for factoring.
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