Question

Yichang

請問這題的快速算法怎麼算？

)下列何者是(x+2)(x+4)(x+6)(x+12)+3x²的因式?
(A) x²-13x-24 (B) x² +13x+24 (C) x²-17x+36
C
(D) x² +17x-36

Answer 1

Mer

(x+2)(x+12)(x+4)(x+6)+3x^2
=(x^2+14x+24)(x^2+10x+24)+3x^2

令x^2+24=y
(14x+y)(10x+y)+3x^2=143x^2+24xy+y^2
十字交乘得(11x+y)(13x+y)
再把y代回得(x^2+11x+24)(x^2+13x+24)
答:B