# Chapter 6 - Section 6.4 - Dividing Polynomials: Long Division and Synthetic Division - Exercise Set - Page 370: 41

$(x-1)(x^2+x+1)$

#### Work Step by Step

The given expression can be written as $x^3-1^3$, which is a difference of two cubes. RECALL: A sum or difference of two cubes can be factored using either of the following formulas: (1) $a^3+b^3=(a-b)(a^2-ab+b^2)$ (2) $a^3-b^3=(a-b)(a^2+ab+b^2)$ Using formula (2) above with $a=x$ and $b=1$ gives: $x^3-1=(x-1)(x^2+x(1)+1^2) = (x-1)(x^2+x+1)$

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