# Chapter R - Elementary Algebra Review - R.4 Polynomials - R.4 Exercise Set: 55

$x^3+4x^2-20x+7$

#### Work Step by Step

Using the Distributive Property, the given expression, $(x+7)(x^2-3x+1) ,$ is equivalent to \begin{array}{l}\require{cancel} x(x^2)+x(-3x)+x(1)+7(x^2)+7(-3x)+7(1) \\\\= x^3-3x^2+x+7x^2-21x+7 \\\\= x^3+(-3x^2+7x^2)+(x-21x)+7 \\\\= x^3+4x^2-20x+7 .\end{array}

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