抱歉，(a)正確問題是：設f(x)=4x2↑ + 14x + 12 及 g(x) = 2x3↑+ 9 x2↑ + 13x + 6 (a) 求 f(x)和g(x)的H.C.F 和L.C.M?

之前你也是問相同的問題，方法都是用因式分解。

(a)
f(x) = 4x² + 14x + 12
= 2(2x² + 7x + 6)
= 2(x + 2)(2x + 3)

g(x) = 2x³ + 9x² + 13x + 6
= 2x³ + 2x² + 7x² + 7x + 6x + 6
= 2x²(x + 1) + 7x(x + 1) + 6(x + 1)
= (x + 1)(2x² + 7x + 6)
= (x + 1)(x + 2)(2x + 3)

H.C.F. = (x + 2)(2x + 3) = 2x² + 7x + 6
〔找相同的因式〕

L.C.M. = 2(x + 1)(x + 2)(2x + 3) = 2g(x) = 4x³ + 18x² + 26x + 12

f(x)=4x^2 +14x+12
f(x)=2(2x^2 +7x+6)
f(x)=2(x+2)(2x+3)
g(x)=2x^3 +9x^2 +13x+6
g(x)=(x+1)(2x+3)(x+2)
H.C.F=(x+2)(2x+3)
L.C.F=2(x+1)(2x+3)(x+2)