(x^2-15x+54)(x^2+11x+28)+350因式分解有速度．．．有过程．．．

Question

(x^2-15x+54)(x^2+11x+28)+350
因式分解
有速度．．．有过程．．．

Answer 1

(x^2-15x+54)(x^2+11x+28)+350
=(x-6)(x-9)(x+4)(x+7)+350
=[(x-6)(x+4)][(x-9)(x+7)]+350
=(x^2-2x-24)(x^2-2x-63)+350
设u=x^2-2x,则
(x^2-2x-24)(x^2-2x-63)+350
=(u-24)(u-63)+350
=u^2-87u+1862
=(u-38)(u-49)
=(x^2-2x-38)(x^2-2x-49)
=(x-1+√39)(x-1-√39)(x-1+5√2)(x-1-5√2)