Final answer:
To factor the polynomial t⁶+t⁵-t⁴-t³, first factor out the common factor of t³, then attempt to factor the remaining quadratic trinomial. The completely factored form is t³(t³+t²-t-1).
Step-by-step explanation:
To factor the polynomial t⁶+t⁵-t⁴-t³, we can first look for common factors. Notice that each term has a common factor of t³, so we can factor that out:
t⁶+t⁵-t⁴-t³ = t³(t³+t²-t-1).
Now, we can try to factor the quadratic trinomial t³+t²-t-1. Unfortunately, there are no simple factors, so we cannot factor it further.
Therefore, the completely factored form of the polynomial t⁶+t⁵-t⁴-t³ is t³(t³+t²-t-1).