Question

How do you divide `(2x^3+28x^2+86x+60)div(x+10)` using synthetic division?

Answer 1

`(2x^3+28x^2+86x+60)div(x+10)=2x^2+8x+6`

Explanation:

#{: ("row 0:",,color(grey)(x^3),color(grey)(x^2),color(grey)(x^1),color(grey)(x^0)), ("row 1:",,2,28,86,60), ("row 2:",ul(+color(white)("x")),ul(color(white)("xxx")),ul(-20),ul(-10),ul(-60)), ("row 3:",xxcolor(blue)(""(-10)),2,8,6,0), ("row 4:",,color(grey)(x^2),color(grey)(x^1),color(grey)(x^0),color(grey)("R")) :}#

rows 0 and 4 are not really part of the synthetic division; they are simply for reference purposes.

row 1 are the coefficients of the terms of the dividend (in cases where the exponent of the variable does not appear in the expression be sure to use `0`)

row 2 is the product of the previous column's value in row 3 times the value required for `x` to make the divisor (`x+10` in this case) equal to `0`.

row 3 is the sum the the values in the corresponding column from rows 1 and 2.

Notice that the exponents of the variable (`x` in this case) have been reduced by `1` fro each column; `color(grey)("R")` is the remainder.

Answer 2

Multiply x+10 by `2x^2+8x+6` and get `2x^3+28x^2+86x+60`, so the answer is `2x^2+8x+6`.

Explanation:

x+10 times `2x^2+8x+6`= `2x^3 +8x^2 + 6x + 20x^2 + 80x + 60`
which by adding like terms is `2x^3+28x^2+86x+60`.