# How do you use synthetic division to find if x+1 is a factor for f(x)=2x^3+5x^2-x-4?

Sep 24, 2015

Using synthetic division as shown below would result in a zero remainder.

#### Explanation:

If: $x + 1$ is a factor then: $x = - 1$ is a root/zero of the polynomial:

$f \left(x\right) = 2 {x}^{3} + 5 {x}^{2} - x - 4$

hence synthetic division should produce a zero remainder.

$\ldots \ldots \ldots . 2 \ldots \ldots . . 5 \ldots \ldots - 1 \ldots - 4$
$- 1 | \downarrow \ldots - 2. \ldots . . - 3. \ldots \ldots . .4$
$\ldots \ldots \ldots . 2. \ldots \ldots . .3 \ldots \ldots - 4. \ldots \ldots .0 \implies$ Remainder

Quotient $= 2 {x}^{2} + 3 x - 4$