Question

Which statements are true about the result of simplifying this polynomial?

Answer 1

To answer the question, we must simplify the following expression:

`t^3(8+9t)-(t^2+4)(t^2-3t)`

We expand the terms in the polynomial using the distributive property for the multiplication:

`8t^3+9t^4-(t^4-3t^3+4t^2-12t)`

Simplifying the last expression we have:

`^{}^{}8t^4+11t^3-4t^2+12t`

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.