To answer the question, we must simplify the following expression:
[tex]t^3(8+9t)-(t^2+4)(t^2-3t)[/tex]
We expand the terms in the polynomial using the distributive property for the multiplication:
[tex]8t^3+9t^4-(t^4-3t^3+4t^2-12t)[/tex]
Simplifying the last expression we have:
[tex]^{}^{}8t^4+11t^3-4t^2+12t[/tex]
We see that the simplified expression:
• is quartic,
,
• doesn't have a constant term,
,
• has four terms,
,
• is a polynomial,
,
• it is not a trinomial.
Answer
The correct answers are:
• The simplified expression has four terms.
,
• The simplified expression is a polynomial.
