# How do you use synthetic division to show that x=-4 is a zero of x^3-28x-48=0?

Aug 24, 2017

See below

#### Explanation:

{: (" ",color(grey)(x^3),color(grey)(x^2),color(grey)(x^1),color(grey)(x^0),color(white)("xxx"),"row 0"), (,1,0,-28,-48,,"row 1"), (ul(color(white)("xx")+color(white)("xxx")),ul(color(white)("xxx")),ul(-4),ul(+16),ul(+48),,"row 2"), (color(blue)(""(-4))xx,1,-4,-12,color(white)("xx")color(red)0,,"row 3") :}

$\text{row 1}$ are the coefficients of the terms of the expression in descending degree (being careful not to omit the term with an implied coefficient of $0$)

The first value in $\text{row 3}$ is the value we are using to evaluate the expression; the remaining values in $\text{row 3}$ are the sum of the numbers in that column from $\text{rows 1}$ and $\text{2}$.

The values in $\text{row 2}$ are the product of our evaluation value and the sum (in $\text{row 3}$) from the previous column.

The final value in $\text{row 3}$ is the value of the expression at the evaluation value.