How do you find the remainder when #(2x^4+6x^3+5x-6) / (x+2)#?

1 Answer
Leland Adriano Alejandro
Mar 21, 2016

We can use synthetic division to find remainder or
We can also use remainder theorem
Remainder #= -32#

Explanation:

#(2x^4+6x^3+5x-6)/(x+2)#
Use synthetic Division

#x^4" " " " " "x^3" " " " " "x^2" " " " " "x^1" " " " "x^0#
#2" " " " " "6" " " " " "0" " " " " "5" " "" " "-6" " "# trial divisor#=-2#
#underline( " " " " " "-4 " " "" " "-4" " " " " "8" " " " "" -26)#
#2 " " " " " " 2 " " " " ""-4 " " " " " "13 " " "" " "-32#

Remainder#=-32#

Also , we can use the remainder theorem
We will use #x=-2# in the dividend

Let #P(x)=2x^4+6x^3+5x-6#
Find #P(-2)#

#P(-2)=2*(-2)^4+6(-2)^3+5(-2)-6#

#P(-2)= -32" " "#and this is the remainder

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