急 F4 MATHS!!!

a)
f(x)=2x^4+11x³-5x²-98x-120
f(-2)=2(-2)^4+11(-2)³-5(-2)²-98(-2)-120
=32-88-20+196-120
=0
By the remainder theorem, f(x) is divisible by x+2

b)
·.·f(x) is divisible by x+2.
By synthetic division,
f(x)=(x+2)(2x³+7x²-19x-60)
Let g(x)=2x³+7x²-19x-60.
g(3)=2(3)³+7(3)²-19(3)-60
=54+63-57-60
=0
By the remainder theorem, g(x) is divisible by x-3
.·.f(x)=(x+2)(2x³+7x²-19x-60)
=(x+2)(x-3)(2x²+13x+20)
=(x-3)(x+2)(x+4)(2x+5)


圖片參考：http://imgcld.yimg.com/8/n/HA08000619/o/701202230084313873440211.jpg


2012-02-23 22:20:17 補充：
Alternative method:
after proving (a) that x+2 is a factor of f(x),
f(x)=(x+2)(2x³+7x²-19x-60)

2x³+7x²-19x-60
=2x³+2x²+5x²-24x+5x-60
=(2x³+2x²-24x)+(5x²+5x-60)
=2x(x²+x-12)+5(x²+x-12)
=(2x+5)(x²+x-12)
=(x-3)(x+4)(2x+5)

.·.f(x)=(x-3)(x+2)(x+4)(2x+5)