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標題:

中四4條maths題...

發問:

1. factorize x^3 + 7x^2 + 15x + 9 2. factorize x^3 - 3x^2 - 10x + 24 3. factorize x^3 - 2x^2 - 23x + 60 4. factorize x^4 - 2x^3 - 7X^2 + 8x +12

最佳解答:

1.) Let f(x) be x3 + 7x2 + 15x + 9. f(-1)= (-1)3 + 7(-1)2 + 15(-1) + 9 = -1+7-15+9 = 0 So, x+1 is a factor of f(x). 圖片參考：http://hk.geocities.com/xangadtb/knowledge/291208/division1.jpg So, x3 + 7x2 + 15x + 9 =(x+1)(x2+6x+9) =(x+1)(x+3)2 2.) Let g(x) be x3 - 3x2 - 10x + 24. g(2)=23 - 3(2)2 - 10*2 + 24 = 8-12-20+24 = 0 So, x-2 is a factor of g(x). 圖片參考：http://hk.geocities.com/xangadtb/knowledge/291208/division2.jpg x3 - 3x2 - 10x + 24 =(x-2)(x2-x-12) =(x-2)(x-4)(x+3) =(x-2)(x+3)(x-4) 3.) Let F(x) be x3 - 2x2 - 23x + 60. F(3)=33 - 2(3)2 - 23*3 + 60=27-18-69+60=0 So, x-3 is a factor of F(x). 圖片參考：http://hk.geocities.com/xangadtb/knowledge/291208/division3.jpg x3 - 2x2 - 23x + 60 =(x-3)(x2+x-20) =(x-3)(x+5)(x-4) =(x-3)(x-4)(x+5) 4.) Let G(x) be x4 - 2x3 - 7x2 + 8x +12. G(2)=24 - 2(2)3 - 7(2)2 + 8(2) +12= 16-16-28+16+12=0 So, x-2 is a factor of G(x). 圖片參考：http://hk.geocities.com/xangadtb/knowledge/291208/division4.jpg x4 - 2x3 - 7x2 + 8x +12 =(x-2)(x3-7x-6) Let f(x) be x3-7x-6. f(3)=33-7*3-6=27-21-6=0 So, (x-3) is a factor of f(x). 圖片參考：http://hk.geocities.com/xangadtb/knowledge/291208/division4a.jpg Thus, x4 - 2x3 - 7x2 + 8x +12 =(x-2)(x3-7x-6) =(x-2)(x-3)(x2+3x+2) =(x-2)(x-3)(x+2)(x+1) =(x+1)(x+2)(x-2)(x-3) 希望幫到你 =]

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其他解答:

Use remainder theorem is ok|||||(1) (x + 3)^2 (x + 1) (2) (x - 4) (x - 2) (x + 3) (3) (x - 4) (x - 3) (x + 5) (4) x^4 - 2x^3 - 7X^2 + 8x +12 = (x^4 - 7X^2 +12) - (2x^3 - 8x) = (x^2 - 4)(x^2 - 3) - 2x(x^2 - 4) = (x^2 - 4)(x^2 - 3 - 2x) = (x^2 - 4)(x^2 - 2x - 3) = (x - 2)(x + 2)(x - 3)(x + 1)