Of course! Let's simplify the polynomial expression [tex]\( x^3 + 4x^2 + 5x + 2 \)[/tex].
1. Identify the polynomial: We begin with the expression [tex]\( x^3 + 4x^2 + 5x + 2 \)[/tex].
2. Combine like terms:
- Since each term in this polynomial [tex]\( x^3, 4x^2, 5x, \text{and} 2 \)[/tex] represents distinct powers of [tex]\( x \)[/tex] and a constant, there are no like terms to combine.
3. Order the terms:
- The polynomial already has its terms in descending order of the power of [tex]\( x \)[/tex] (from [tex]\( x^3 \)[/tex] to the constant term).
4. Check for factorization or common factors:
- This polynomial does not have any common factors among its terms that can be factored out and cannot be factored into simpler polynomial products easily.
Thus, the expression [tex]\( x^3 + 4x^2 + 5x + 2 \)[/tex] is already in its simplest form.
So the simplified form of the polynomial is:
[tex]\[
x^3 + 4x^2 + 5x + 2
\][/tex]
