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

1 Answer
Aug 24, 2017

Answer:

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.