\( \left. \begin{array} { l } { ( x ^ { 4 } - 2 x ^ { 2 } + 2 ) \cdot ( x ^ { 2 } - 2 x + 3 ) = } \\ { ( 3 x ^ { 2 } - 5 x ) \cdot ( 2 x ^ { 3 } + 4 x ^ { 2 } - x + 2 ) = } \end{array} \right. \)

The expression \( \left( x ^ { 4 } - 2 x ^ { 2 } + 2 \right) \cdot \left( x ^ { 2 } - 2 x + 3 \right) \) can be simplified by recognizing that the first term is a quadratic in disguise. By letting \( y = x^2 \), we can reframe \( x^4 - 2x^2 + 2 \) as \( (y - 1)^2 + 1 \). This makes factoring and finding roots easier! On the flip side, when you tackle \( \left( 3 x ^ { 2 } - 5 x \right) \cdot \left( 2 x ^ { 3 } + 4 x ^ { 2 } - x + 2 \right) \), it’s all about the distribution! Don’t forget to distribute each term carefully to avoid misplaced signs and terms; it’s a common pitfall to mix them up when multiplying polynomials. Double-checking your addition is a surefire way to avoid errors in the final equation!