# What is the first term of the quotient of the following division problem (x^3-1)div(x+2)?

Aug 20, 2017

${x}^{2}$

#### Explanation:

Expression $= \frac{{x}^{3} - 1}{x + 2}$

By synthetic division of polynomials:

Expression $= {x}^{2} - 2 x + 2 - \left(\frac{5}{x + 2}\right)$

Hence, the first term of the quotient is ${x}^{2}$

Aug 21, 2017

${x}^{2}$

#### Explanation:

$\text{using the divisor as a factor in the numerator}$

$\text{consider the numerator}$

$\textcolor{red}{{x}^{2}} \left(x + 2\right) \textcolor{m a \ge n t a}{- 2 {x}^{2}} - 1$

$= \textcolor{red}{{x}^{2}} \left(x + 2\right) \textcolor{red}{- 2 x} \left(x + 2\right) \textcolor{m a \ge n t a}{+ 4 x} - 1$

$= \textcolor{red}{{x}^{2}} \left(x + 2\right) \textcolor{red}{- 2 x} \left(x + 2\right) \textcolor{red}{+ 4} \left(x + 2\right) \textcolor{m a \ge n t a}{- 8} - 1$

$= \textcolor{red}{{x}^{2}} \left(x + 2\right) \textcolor{red}{- 2 x} \left(x + 2\right) \textcolor{red}{+ 4} \left(x + 2\right) - 9$

$\text{quotient "=color(red)(x^2-2x+4)," remainder } = - 9$

$\text{first term of the quotient } = {x}^{2}$