十万里加急！！！ 高中数学题！！！！！ 求助 大神， 希望有高人 耐心指点， thx 希望　我能早早的　被　贵人　找到！?

求解下题 并 提供 列式, 列式，因为这很重要， 能解说一下更好

Question No.1

Inquiry and Investigation

6.1 : Exploring the limitations of using the Factor Theorem to find the factors of a polynomial

Inquiry
Is the Factor Theorem always useful in factorizing the polynomial (尼度打唔度出来，只能。。) ax(3)+bx(2)+cx+d (即: a乘x的三次方 + b乘x的二次方 +c乘x + d ) into a product of linear factors?

Investigation Steps

1. Let (这里指函数) f(x) = x(3次方)+3x(2次方) -x-3.

(a) List all the possible linear factors of f(x).

(b) Using the Factor Theorem, determine whether each expression obtained in (a) is a factor of f(x).

(c) If we do not use long division, can f(x) be factorized into a product of linear factors? If yes, factorize f(x).

2. Let (这里指函数) g(x)= x(3次方) -2x(2次方) +7x-6.

(a) List all the possible linear factors of g(x).

(b)Using the Factor Theorem, determine whether each expression obtained in (a) is a factor of g(x).

(c) If we do not use long division, can g(x) be factorized into a product of linear factors? If yes, factorize g(x).

Conclusion

The Factor Theorem is (always / not always) useful in factorizing the polynomial ax(3)+bx(2)+cx+d (即: a乘x的三次方 + b乘x的二次方 +c乘x + d ) .

此题除求解外， 真心想知道 它背后想说什么，想教 我 什么。 (c) 部分，不用长除， f(x) 怎么被 factorized？ ‘’怎么‘’？ 它书中从未就此说过怎么。
还有， 我 忘了 什 么是 linear， linear factor 是怎样？（带x（1次方）？）另外还有什么玄机 诚望指出。