Direct Substitution : f(x) = f(-3) = -(-3^4) + (-3)^3 -(-3) + 1f(x)=f(−3)=−(−34)+(−3)3−(−3)+1
f(-3) = = -81 - 27 +3 +1 = -104f(−3)==−81−27+3+1=−104
Synthetic Division :
color(white)(aa)-3color(white)(aa)|color(white)(aa)-1color(white)(aaa)1color(white)(aaaaa)0color(white)(aa)-1color(white)(aaaaa)1aa−3aa∣aa−1aaa1aaaaa0aa−1aaaaa1
color(white)(aaaaaaaa)|color(white)(aaa)darrcolor(white)(aaa)3color(white)(a)-12color(white)(aaaa)36color(white)(a)-105aaaaaaaa∣aaa⏐↓aaa3a−12aaaa36a−105
color(white)(aaaaaaa)------------aaaaaaa−−−−−−−−−−−−
color(white)(aaaaaaaaaaa)-1color(white)(aaaa)4color(white)(a)-12color(white)(aaaa)35color(white)(a)-104aaaaaaaaaaa−1aaaa4a−12aaaa35a−104
Quotient color(green)(Q = -x^3 + 4x^2 - 12x + 35)Q=−x3+4x2−12x+35, Remainder color(red)(R = (-104)/(x+3))R=−104x+3