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

1 Answer
sankarankalyanam
Jan 30, 2018

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)

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