To determine the degree of the polynomial [tex]\( t - 4t^2 + 2t^3 \)[/tex], we follow these steps:
1. Identify the Terms: Begin by listing all the terms in the polynomial:
[tex]\[
t, \quad -4t^2, \quad 2t^3
\][/tex]
2. Determine the Degree of Each Term:
- The term [tex]\( t \)[/tex] has a degree of 1 (since [tex]\( t \)[/tex] is the same as [tex]\( t^1 \)[/tex]).
- The term [tex]\( -4t^2 \)[/tex] has a degree of 2 (since the exponent of [tex]\( t \)[/tex] is 2).
- The term [tex]\( 2t^3 \)[/tex] has a degree of 3 (since the exponent of [tex]\( t \)[/tex] is 3).
3. Find the Highest Degree:
- The degrees of the terms are 1, 2, and 3.
4. Determine the Degree of the Polynomial:
- The highest degree among the terms is 3.
Therefore, the degree of the polynomial [tex]\( t - 4t^2 + 2t^3 \)[/tex] is [tex]\( \boxed{3} \)[/tex].
