# How do you divide (x^3 - 7x - 6)/(x+1)?

Apr 9, 2018

Quotient is ${x}^{2} - x - 6$ and remainder is $0$

#### Explanation:

${x}^{3} - 7 x - 6$

=${x}^{3} + {x}^{2} - {x}^{2} - x - 6 x - 6$

=${x}^{2} \cdot \left(x + 1\right) - x \cdot \left(x + 1\right) - 6 \cdot \left(x + 1\right)$

=$\left({x}^{2} - x - 6\right) \cdot \left(x + 1\right)$

Hence quotient is ${x}^{2} - x - 6$ and remainder is $0$