# How do you use polynomial synthetic division to divide (18x^2-15x-25)div(x-5/3) and write the polynomial in the form p(x)=d(x)q(x)+r(x)?

Dec 30, 2017

The answer is $= \left(x - \frac{5}{3}\right) \left(18 x + 15\right) + 0$

#### Explanation:

Perform the synthetic division

$\textcolor{w h i t e}{a a a a}$$\frac{5}{3}$$\textcolor{w h i t e}{a a a a}$$|$$18$$\textcolor{w h i t e}{a a a a}$$- 15$$\textcolor{w h i t e}{a a a a}$$- 25$

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a}$$|$$\textcolor{w h i t e}{a a a a a a a a}$$30$$\textcolor{w h i t e}{a a a a a a}$$25$

$\textcolor{w h i t e}{a a a a}$$\textcolor{w h i t e}{a a a a a a}$$|$$18$$\textcolor{w h i t e}{a a a a a a}$$15$$\textcolor{w h i t e}{a a a a a a a}$$0$

Therefore,

$18 {x}^{2} - 15 x - 25 = \left(x - \frac{5}{3}\right) \left(18 x + 15\right) + 0$

The quotient is $= 18 x + 15$ and the remainder is $= 0$