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

1 Answer
Jan 30, 2018

Answer:

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)#