# How do you use synthetic division to determine if -1 is a lower bound of f(x) = 4x^3-2x^2+2x-4?

Oct 6, 2017

$Q u o t i e n t = 4 {x}^{2} + 2 x + 4$ & Remainder $= 0$

#### Explanation:

(4x^3-2x^2+2x-4)/((x-1) using synthetic division:
1 | 4 -2 2 -4
| 4 2 4
___
| 4 2 4 0
Quotient $= 4 {x}^{2} + 2 x + 4$ & Remainder $= 0$

Verification:
$f \left(1\right) = 4 - 2 + 2 - 4 = 0$