Final answer:
The polynomial f(x) = x³ + 22x + 6 = 0 has three linear factors, corresponding to its degree. These factors might be real or complex and can be found using various algebraic methods, though complex roots may require numerical solutions.
Step-by-step explanation:
The polynomial in question, f(x) = x³ + 22x + 6 = 0 (after correcting the typo), is a third-degree polynomial, and therefore, it will have three linear factors. This is because the Fundamental Theorem of Algebra states that a polynomial of degree n will have exactly n roots (or zeros), and each root corresponds to a linear factor of the form (x - root). However, these linear factors can be real or complex.
To find the specific linear factors, one would typically use methods like factoring by grouping, synthetic division, the Rational Root Theorem, or numerical methods if the roots cannot be found algebraically. For some equations, such as the quadratic equation x² + 0.0211x - 0.0211 = 0, the quadratic formula could be used to find the two linear factors. But for cubic equations, the process can be more complex and may not always result in simple expressions for the factors.