Question

question 1 of 10
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^2 ) is negative
c. when the coefficient of ( x ) is negative

Explanation:

To determine when to factor out -1 from a trinomial (a quadratic of the form \(ax^2 + bx + c\)), we analyze each option:

• Option A: A negative constant term (\(c<0\)) doesn’t require factoring out -1. Factoring for a negative constant focuses on finding two numbers with opposite signs, not factoring out -1.
• Option B: If the coefficient of \(x^2\) (\(a\)) is negative, factoring out -1 makes \(a\) positive (e.g., \(-2x^2 + 3x + 4 = -1(2x^2 - 3x - 4)\)). This is a common practice to simplify factoring, as factoring is easier with a positive leading coefficient.
• Option C: A negative coefficient of \(x\) (\(b<0\)) doesn’t necessitate factoring out -1. Adjusting signs of factors or using other factoring methods (like AC method) can handle negative \(b\) without factoring out -1.

Thus, factoring out -1 is most likely when the \(x^2\) coefficient is negative.

Answer:

B. When the coefficient of \(x^2\) is negative