In which situation would you most likely factor out -1 from a trinomial?
A. When the constant term is negative
B. When the coefficient of x is negative
C. When the coefficient of x² is negative
Answer (2)
The most likely situation to factor out -1 from a trinomial is when the coefficient of x 2 is negative, as it simplifies the trinomial for further factoring. Therefore, the selected answer is C.
;
Factoring out -1 from a trinomial changes the signs of all terms.
This is most useful when the coefficient of x 2 is negative, making it positive.
This simplifies factoring the trinomial.
Therefore, the answer is C.
Explanation
Understanding the Question We are given a multiple-choice question asking when it is most likely to factor out -1 from a trinomial. The options are:
A. When the constant term is negative B. When the coefficient of x is negative C. When the coefficient of x² is negative
Analyzing the Trinomial Consider a general trinomial a x 2 + b x + c . Factoring out -1 results in − ( − a x 2 − b x − c ) . If a < 0 , then 0"> − a > 0 , so factoring out -1 makes the coefficient of x 2 positive. This is often done to simplify factoring when the leading coefficient is negative.
Determining the Most Likely Situation If the constant term is negative, factoring out -1 makes it positive, but this isn't always helpful. If the coefficient of x is negative, factoring out -1 makes it positive, but this isn't always helpful. Therefore, the most likely situation is when the coefficient of x 2 is negative.
Final Answer The most likely situation to factor out -1 from a trinomial is when the coefficient of x 2 is negative. So the answer is C.
Examples
Factoring out a -1 can be useful in physics when dealing with energy equations. For example, if you have an equation for potential energy that starts with a negative leading coefficient, factoring out the -1 can make it easier to analyze the system's stability and behavior. This simplifies calculations and helps in understanding the underlying physical principles.
