The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.
Polynomials can be expressed as a product of binomials of the form (x - r) multiplied by a leading coefficient. The least polynomial contain the number of roots presented in statement, whose factor form is shown below:
f(x) = 1 · (x + 3)³ · x³ · (x - 3)
f(x) = (x + 3)³ · (x⁴ - 3 · x³)
f(x) = (x³ + 9 · x² + 27 · x + 27) · (x⁴ - 3 · x³)
f(x) = x⁷ + 9 · x⁶ + 27 · x⁵ + 27 · x⁴ - 3 · x⁶ - 27 · x⁵ - 81 · x⁴ - 81 · x³
f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³
The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.
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