# Using synthetic division, what is the quotient and the remainder for polynomial P(x) = x^3 - 2x^2 - 5x +6 divided by (x-1)?

Nov 20, 2017

$\left({x}^{2} - x - 6\right)$

#### Explanation:

we need ${x}^{3}$ so we add ${x}^{2}$

$\implies$
(x-1)(x^2
$\implies {x}^{3} - {x}^{2}$
we need $- 2 {x}^{2}$ so we add $- x$

$\implies$
(x-1)(x^2-x
$\implies {x}^{3} - {x}^{2} - {x}^{2} + x$
we need $- 5 x$ so we add $- 6$

$\implies$
(x-1)(x^2-x-6
${x}^{3} - {x}^{2} - {x}^{2} + x - 6 x + 6$

we have what we need so we can close it

$\implies$
$\left(x - 1\right) \left({x}^{2} - x - 6\right)$
${x}^{3} - 2 {x}^{2} + 5 x + 6$

$\implies$
$\frac{{x}^{3} - 2 {x}^{2} + 5 x + 6}{x - 1} = \left({x}^{2} - x - 6\right)$