To determine the various characteristics of the polynomial [tex]\( h(x) = 1.6x - 0.59 \)[/tex], we need to examine each component of the expression.
1. Leading Term:
- The leading term is the term with the highest power of [tex]\( x \)[/tex] in the polynomial. In this case, [tex]\( 1.6x \)[/tex] is the term with the highest power of [tex]\( x \)[/tex], which is 1.
Therefore, the leading term of the polynomial [tex]\( h(x) = 1.6x - 0.59 \)[/tex] is [tex]\( 1.6x \)[/tex].
[tex]\[
\text{The leading term of the polynomial } h(x) = 1.6x - 0.59 \text{ is } 1.6x.
\][/tex]
2. Leading Coefficient:
- The leading coefficient is the coefficient of the leading term. Here, the coefficient of [tex]\( 1.6x \)[/tex] is [tex]\( 1.6 \)[/tex].
Therefore, the leading coefficient of the polynomial [tex]\( h(x) = 1.6x - 0.59 \)[/tex] is [tex]\( 1.6 \)[/tex].
[tex]\[
\text{The leading coefficient of the polynomial } h(x) = 1.6x - 0.59 \text{ is } 1.6.
\][/tex]
3. Degree:
- The degree of the polynomial is the highest power of [tex]\( x \)[/tex] in the polynomial. In this case, the highest power of [tex]\( x \)[/tex] is 1 (from the term [tex]\( 1.6x \)[/tex]).
Therefore, the degree of the polynomial [tex]\( h(x) = 1.6x - 0.59 \)[/tex] is [tex]\( 1 \)[/tex].
[tex]\[
\text{The degree of the polynomial } h(x) = 1.6x - 0.59 \text{ is } 1.
\][/tex]
4. Classification:
- The classification of a polynomial is based on its degree:
- Constant (degree 0)
- Linear (degree 1)
- Quadratic (degree 2)
- Cubic (degree 3)
- Quartic (degree 4)
Since the degree of the polynomial [tex]\( h(x) = 1.6x - 0.59 \)[/tex] is 1, it is classified as a linear polynomial.
[tex]\[
\text{The polynomial is linear.}
\][/tex]
In summary:
[tex]\[
\text{The leading term of the polynomial } h(x) = 1.6x - 0.59 \text{ is } 1.6x.
\][/tex]
[tex]\[
\text{The leading coefficient of the polynomial } h(x) = 1.6x - 0.59 \text{ is } 1.6.
\][/tex]
[tex]\[
\text{The degree of the polynomial } h(x) = 1.6x - 0.59 \text{ is } 1.
\][/tex]
[tex]\[
\text{The polynomial is linear.}
\][/tex]
