多项式2x^4-x^3-6x^2-x+2的因式分解为(2x-1)q(x),则q(x)等于?(A) (x+2)(2x-1)^2(B) (x-2)(x^2+1)(C) (2x+1)(x^2-2)(D) (2x-1)^2(x+2)(E) (2x+1)^2(x-2)

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多项式2x^4-x^3-6x^2-x+2的因式分解为(2x-1)q(x),则q(x)等于?(A) (x+2)(2x-1)^2(B) (x-2)(x^2+1)(C) (2x+1)(x^2-2)(D) (2x-1)^2(x+2)(E) (2x+1)^2(x-2)
多项式2x^4-x^3-6x^2-x+2的因式分解为(2x-1)q(x),则q(x)等于?
(A) (x+2)(2x-1)^2
(B) (x-2)(x^2+1)
(C) (2x+1)(x^2-2)
(D) (2x-1)^2(x+2)
(E) (2x+1)^2(x-2)

多项式2x^4-x^3-6x^2-x+2的因式分解为(2x-1)q(x),则q(x)等于?(A) (x+2)(2x-1)^2(B) (x-2)(x^2+1)(C) (2x+1)(x^2-2)(D) (2x-1)^2(x+2)(E) (2x+1)^2(x-2)
=2x^4-x³-6x²+3x-4x+2
=x³(2x-1)-3x(2x-1)-2(2x-1)
=(2x-1)(x³-3x-2)
∴q(x)=x³-3x-2

q(x)=x^3-3x-2

2x^4-x^3-6x^2-x+2=x^3(2x-1)-(2x-1)(3x+2)=(2x-1)(x^3-3x-2)
q(x)=x^3-3x-2=x^3-8-3x+6=(x-2)(x^2+2x+4)-3(x-2)=(x-2)(x^2+2x+1)=(x-2)(x+1)^2

2x^4-x^3-6x^2-x+2=(2x^4-x^3)-(6x^2+x-2)=x^3(2x-1)-(2x-1)(3x+2)=(2x-1)(x^3-3x-2)=(2x-1)q(x)

2x^4-x^3-6x^2-x+2
=(2x-1)x^3-(2x-1)(3x+2)
=(2x-1)(x^3-3x-2)
q(x)=x^3-3x-2