To analyze the given polynomial [tex]\( -\frac{1}{6} + 10x^3 \)[/tex], let's break it down into its constituent terms and components.
1. Identify the Terms:
- The polynomial has two terms:
- The first term is a constant: [tex]\(-\frac{1}{6}\)[/tex].
- The second term is [tex]\(10x^3\)[/tex], where 10 is the coefficient, and [tex]\(x^3\)[/tex] represents [tex]\(x\)[/tex] raised to the power of 3.
2. Constant Term:
- The constant term in the polynomial is [tex]\(-\frac{1}{6}\)[/tex]. This term does not involve the variable [tex]\(x\)[/tex] and remains unchanged regardless of the value of [tex]\(x\)[/tex].
3. Coefficient of [tex]\(x^3\)[/tex] Term:
- The coefficient of the [tex]\(x^3\)[/tex] term is 10. This means that for the term involving [tex]\(x\)[/tex] cubed, 10 is the multiplicative factor. In other words, 10 times [tex]\(x^3\)[/tex].
4. Combining Information:
- The polynomial can thus be expressed explicitly with these components: a constant term [tex]\(-\frac{1}{6}\)[/tex] and a term involving [tex]\(x\)[/tex] with a coefficient of 10 in front of [tex]\(x^3\)[/tex].
Hence, from our analysis:
- The constant term is [tex]\(-\frac{1}{6}\)[/tex], which is approximately [tex]\(-0.16666666666666666\)[/tex].
- The coefficient of [tex]\(x^3\)[/tex] is 10.
Therefore, the results from analyzing the polynomial are:
- Constant term: [tex]\(-0.16666666666666666\)[/tex]
- Coefficient of [tex]\(x^3\)[/tex] term: 10
