
SAT II Math level 2
Hi, my exam is nov1 n im really panicking even the easiest things dont make sense Here's the problem x³ − 4x² + 2x + 4 = (x² − 2x − 2)(x − 2)
apparently the roots of this is supposed to be 2, 1+the root of 3 sry cant find the symbol can u explain why?

$\displaystyle y = x^3 4x^2 +2x + 4$
Finding the roots is equivalent to finding the xintercepts of its graph and this is done by setting y = 0:
$\displaystyle \begin{array}{rcl}0 & = & x^3  4x^2 + 2x + 4 \\ 0 & = & (x^2  2x 2)(x2) \end{array}$
If the product of two integers is equal to 0, then either one or both are 0. Let's see what x values would make each factor equal to 0:
$\displaystyle 0 = x  2 \ \leftrightarrow \ x = 2$ So one root is x = 2.
As for the other one, it requires the quadratic formula:
$\displaystyle \begin{array}{rcl} 0 & = & x^2  2x  2 \\ x & = & \displaystyle\frac{(2) \pm \sqrt{(2)^2  4(1)(2)}}{2(1)} \quad \text{By the quadratic formula} \\ x & = & \displaystyle \frac{2 \pm \sqrt{12}}{2} \\ & \vdots &\end{array}$
Simplify the radical and you'll get your desired answer.