Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set - Page 344: 13

$(x-5)^2(x+5)$

Work Step by Step

Using factoring by grouping, the factored form of the given expression, $x^3-5x^2-25x+125 ,$ is \begin{array}{l} (x^3-5x^2)-(25x-125) \\\\= x^2(x-5)-25(x-5) \\\\= (x-5)(x^2-25) .\end{array} Using $a^2-b^2=(a+b)(a-b)$, the expression above is further factored as \begin{array}{l} (x-5)(x+5)(x-5) \\\\= (x-5)^2(x+5) .\end{array}

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