(1) Find the remainder R by long division
(2x^4 - 10x^2 + 30x - 60) ÷ (x + 4)
2x^3 - 8x^2 + 22x - 58
(2x^4 + 0 - 10x^2 + 30x - 60)
(x + 4) 2x^4 + 8x^3
-8x^3 - 10x^2
-8x^3 - 32x^2
22x^2 + 30x
22x^2 + 88x
- 58x - 60
- 58x - 232
172
(2x^4 - 10x^2 + 30x - 60) ÷ (x + 4)= 2x^3 - 8x^2 + 22x - 58 .R=172
(2) Find the remainder R by the remainder theorem
R = f(-4) = 2*(-4)^4 - 10*(-4)^2 +30*(-4) - 60 = 172
备注：忽略了“and by the remainder theorem”.