Certainly! Let's work through the expression [tex]\( -x^2 \)[/tex] step-by-step.
1. Identify the structure of the expression:
The given expression is [tex]\( -x^2 \)[/tex]. This can be recognized as a polynomial of degree 2 (a quadratic term).
2. Understanding the role of each component in the polynomial:
- The term [tex]\( x^2 \)[/tex] denotes the variable [tex]\( x \)[/tex] raised to the power of 2.
- The [tex]\( - \)[/tex] sign indicates that the entire term [tex]\( x^2 \)[/tex] is being negated.
- Therefore, the expression can be viewed as [tex]\( -1 \cdot x^2 \)[/tex], where [tex]\( -1 \)[/tex] is multiplying [tex]\( x^2 \)[/tex].
3. Determining the coefficient:
In polynomial expressions, a coefficient is the numerical factor that is multiplied by the variable term. Here, we identify that [tex]\( -1 \)[/tex] is the numerical factor multiplying [tex]\( x^2 \)[/tex].
Hence, [tex]\( -1 \)[/tex] is the coefficient of [tex]\( x^2 \)[/tex] in the expression [tex]\( -x^2 \)[/tex].
So, to answer the question:
In an expression such as [tex]\( -x^2 \)[/tex], we know that [tex]\( -1 \)[/tex] is understood to be the coefficient of [tex]\( x^2 \)[/tex].
