# Chapter 4 - Polynomials - Mid-Chapter Review - Mixed Review: 20

$-x^5+2x^4-2x^2-x$

#### Work Step by Step

By combining like terms, the given expression, $\left(x^4-2x^2-\dfrac{1}{2}x \right)-\left( x^5-x^4+\dfrac{1}{2}x \right)$, simplifies to \begin{array}{l}\require{cancel} x^4-2x^2-\dfrac{1}{2}x-x^5+x^4-\dfrac{1}{2}x \\\\= -x^5+(x^4+x^4)-2x^2+\left( -\dfrac{1}{2}x-\dfrac{1}{2}x \right) \\\\= -x^5+2x^4-2x^2-x .\end{array}

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