Question

How do you use synthetic division to find x=2 for `P(x) = x^4+x^2+x-6`?

Answer 1

Substitution : `color(blue)(P(x) = P(2) = 20)`

Synthetic Division :
Quotient `color(brown)(Q = x^3 + 2x^2 + 5x + 11)`, Remainder `color(red)(R = 16/(x-2)`

Explanation:

`P(x) = x^4 + x^2 + x - 6` for `x = 2`

`P(x) = P(2) = 2^4 + 2^2 + 2 - 6 = 20`

`color(white)(aa)2color(white)(aa)|color(white)(aa)1color(white)(aa)0color(white)(aa)1color(white)(aa)1color(white)(aa)-6`
`color(white)(aaaaaa)|darrcolor(white)(aa)2color(white)(aa)4color(white)(a)10color(white)(aaa)22`
`color(white)(aaaaa)--------`
`color(white)(aaaaaaaaa)1color(white)(aa)2color(white)(aa)5color(white)(a)11color(white)(aaa)16`

Quotient `color(brown)(Q = x^3 + 2x^2 + 5x + 11)`, Remainder `color(red)(R = 16/(x-2)`