Answer
$4x^{4}-4x^{3}+6x^{2}-\displaystyle \frac{17}{2}x+3$
Work Step by Step
Multiply each term of one polynomial with the terms of the other polynomial,
and combine like terms
$\left.\begin{array}{cllllll}
x(4x^{3}-2x^{2}+5x-6) = & 4x^{4} & -2x^{3} & +5x^{2} & -6x & \\
+ & & & & & \\
-\frac{1}{2}(4x^{3}-2x^{2}+5x-6) = & & -2x^{3} & +x^{2} & -\frac{5}{2}x & +3
\end{array}\right.$
Combining like terms,
=$4x^{4}-4x^{3}+6x^{2}-\displaystyle \frac{17}{2}x+3$