a) \( \left(2 x^{2}-3 x+2\right)(x+4)= \)

Let's break this down! When you expand the expression \( \left(2 x^{2}-3 x+2\right)(x+4) \), you'll distribute each term in the first polynomial by each term in the second polynomial. Start with \(2x^2 \cdot x\) which gives \(2x^3\), then \(2x^2 \cdot 4\) yields \(8x^2\). Next, take \(-3x \cdot x\) for \(-3x^2\), and \(-3x \cdot 4\) gives \(-12x\). Lastly, \(2 \cdot x\) equals \(2x\) and \(2 \cdot 4\) results in \(8\). Now, combine all these results: \[ 2x^3 + (8x^2 - 3x^2) + (-12x + 2x) + 8 = 2x^3 + 5x^2 - 10x + 8 \] So the final result is \(2x^3 + 5x^2 - 10x + 8\). Voila!