Express x^11 + 2 as a trinomial in standard form.
Understand the Problem
The question is asking how to express the polynomial x^11 + 2 as a trinomial in standard form, which typically means rewriting it in the format ax^2 + bx + c.
Answer
The polynomial can be expressed as $0x^2 + 0x + (x^{11} + 2)$.
Answer for screen readers
The polynomial can be expressed as $0x^2 + 0x + (x^{11} + 2)$.
Steps to Solve
- Recognize the form of a trinomial
A trinomial in standard form is written as $ax^2 + bx + c$. Since $x^{11} + 2$ is already a polynomial, we need to express it in terms of a trinomial.
- Identify the highest degree term
The term $x^{11}$ is the highest degree term, where $a = 1$ and it cannot fit into the $ax^2$ term directly.
- Correctly express the polynomial
Since there is no $x^2$ or $x$ term, we rewrite the polynomial as:
$$ 0x^2 + 0x + 2 + x^{11} $$
This means:
- The coefficient of $x^2$ (b) is 0
- The coefficient of $x$ (c) is 0
- The constant term is just $2$
- Combine the terms
Thus, we express the polynomial as:
$$ x^{11} + 0x^2 + 0x + 2 $$
However, for this task, we generally focus on showing our expression as a trinomial. Therefore, the simplest trinomial representation is:
$$ 0x^2 + 0x + (x^{11} + 2) $$
The polynomial can be expressed as $0x^2 + 0x + (x^{11} + 2)$.
More Information
This representation highlights that while the polynomial includes a term of degree 11, the coefficients for $x^2$ and $x$ are both zero, indicating those terms are missing in the trinomial.
Tips
- Assuming all terms have to be filled: It's important to understand that a trinomial can have coefficients of zero, which means those terms may be completely absent.
- Forgetting to include all parts of the trinomial: Always ensure you state all three parts, even if two are zero.
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