分解因式(x-4x-12)(x-4x+3)+56

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分解因式(x-4x-12)(x-4x+3)+56
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分解因式(x-4x-12)(x-4x+3)+56
分解因式(x-4x-12)(x-4x+3)+56

分解因式(x-4x-12)(x-4x+3)+56
=(x^2-4x-12)(x^2-4x-12+15)+56
= (x^2-4x-12)^2+15(x^2-4x-12)+56
= (x^2-4x-12+7)(x^2-4x-12+8)
=(x^2-4x-5) (x^2-4x-4)
=(x+1)(x-5)(x^2-4x-4)
有理数范围内只能这样了

(x^2-4x-12)(x^2-4x+3)+56
=(x^2-4x)^2+(-12+3)(x^2-4x)-36+56
=(x^2-4x)^2-9(x^2-4x)+20
=(x^2-4x-4)(x^2-4x-5)
=(x-2+2√2)(x-2-2√2)(x+1)(x-5)