A trinomial is an algebraic expression that consists of three terms. To determine if the given expression qualifies as a trinomial, we first need to break down the expression provided:
Let’s simplify the expression:
x³ + x² + 1 + 2x³ + x² + 4x³ + x² + 1x + 6x + 6
Now, combine like terms:
- For x³ terms: 1x³ + 2x³ + 4x³ = 7x³
- For x² terms: 1x² + 1x² + 1x² = 3x²
- For x terms: 1x + 6x = 7x
- Constant term: 6
Putting it all together, we get:
7x³ + 3x² + 7x + 6
We now have four terms in the simplified expression, therefore it is not a trinomial. A trinomial must have exactly three terms, whereas our simplified expression contains four: 7x³, 3x², 7x, and 6.
In summary, the expression provided simplifies to a polynomial with four terms, so it is not a trinomial.