How do you divide using synthetic division: (2x^3 - 4x^2 - 7x + 5)/(x - 3)?

Feb 21, 2017

The remainder is $= 2$ and the quotient is $= 2 {x}^{2} + 2 x - 1$

Explanation:

We perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$3$$\textcolor{w h i t e}{a a a a}$$|$$\textcolor{w h i t e}{a a a a}$$2$$\textcolor{w h i t e}{a a a a}$$- 4$$\textcolor{w h i t e}{a a a a a}$$- 7$$\textcolor{w h i t e}{a a a}$$5$

$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a}$$|$$\textcolor{w h i t e}{a a a}$$\textcolor{w h i t e}{a a a a a a a a}$$6$$\textcolor{w h i t e}{a a a a a a}$$6$$\textcolor{w h i t e}{a a a}$$- 3$

$\textcolor{w h i t e}{a a a a a a a a a a}$------------------------------------------------------------

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a}$$\textcolor{w h i t e}{a a a a a a}$$2$$\textcolor{w h i t e}{a a a a}$$2$$\textcolor{w h i t e}{a a a a a}$$- 1$$\textcolor{w h i t e}{a a a a a}$$\textcolor{red}{2}$

The remainder is $= 2$

The quotient is $= 2 {x}^{2} + 2 x - 1$

Verification, by using the remainder theorem

$f \left(3\right) = 54 - 36 - 21 + 5 = 59 - 57 = 2$