Question

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

Answer 1

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") :}`

`"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 `"row 3"` is the value we are using to evaluate the expression; the remaining values in `"row 3"` are the sum of the numbers in that column from `"rows 1"` and `"2"`.

The values in `"row 2"` are the product of our evaluation value and the sum (in `"row 3"`) from the previous column.

The final value in `"row 3"` is the value of the expression at the evaluation value.