7x^4+20x^3+11x^2+40-6因式分解快
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7x^4+20x^3+11x^2+40-6因式分解快
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![7x^4+20x^3+11x^2+40-6因式分解快](/uploads/image/z/18853775-71-5.jpg?t=7x%5E4%2B20x%5E3%2B11x%5E2%2B40-6%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%E5%BF%AB)
7x^4+20x^3+11x^2+40x-6
=7x^4+21x^3-x^3-3x^2+14x^2+42x-2x-6
=7x^3(x+3)-x^2(x+3)+14x(x+3)-2(x+3)
=(x+3)(7x^3-x^2+14x-2)
=(x+3)[x^2(7x-1)+2(7x-1)]
=(x+3)(7x-1)(x^2+2)
=7x^4+21x^3-x^3-3x^2+14x^2+42x-2x-6
=7x^3(x+3)-x^2(x+3)+14x(x+3)-2(x+3)
=(x+3)(7x^3-x^2+14x-2)
=(x+3)[x^2(7x-1)+2(7x-1)]
=(x+3)(7x-1)(x^2+2)