Roots of a Cubic Polynomial

Very Hard Advanced Math Polynomial Expressions

Consider the polynomial expression $P(x) = 4x^3 - 12x^2 + 9x - 1$.

What is the value of $x$ for which $P(x) = 0$?

Additionally, if you find one root, use synthetic division to express $P(x)$ as a product of its linear factors and identify all roots of the polynomial.

The only root is $x = 1$.

The roots are $x = 1, x = \frac{3}{2} + \frac{\sqrt{3}}{2}i, x = \frac{3}{2} - \frac{\sqrt{3}}{2}i$.

The roots are $x = \frac{1}{2}, x = 2, x = \frac{3}{2}$.

The roots are $x = 3, x = -\frac{1}{4} + \frac{\sqrt{3}}{4}i, x = -\frac{1}{4} - \frac{\sqrt{3}}{4}i$.

Hint

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