Question

因式分解：2x^4-x^3+2x^2+1 x^4-3x^2+4x-3 x^4+x^3+2x^2-x+3 a^2(b-c)+b^2(c-a)+c^2(a-b)

Answer 1

(1)、2X^4-X^3+2X^2+1
=2X^4-2X^3+2X^2+x^3+1
=2x^2(x^2-x+1)+(x+1)(x^2-x+1)
=(2x^2+(x+1))(x^2-x-1)
=(2x^2+x+1) (x^2-x+1)

(2)、x^4-3x^2+4x-3
=x^4-3x^2+3x+x-3
=x^4-x^3+x^2+x^3-x^2+x-3x^2+3x-3
=(x^2 + x - 3)(x^2 - x + 1)

(3)、x^4+x^3+2x^2-x+3
=x^4+x^3+2x^2+2x-2x-x+3
=x^3(x+1)+2x(x+1)-3(x+1)
=(x+1)(x^3+2x-3)

(4)、a^2(b-c)+b^2(c-a)+c^2(a-b)
=a^2b-a^2c+b^2c-ab^2+ac^2-bc^2
=a^2b-ab^2+b^2c-a^2c+ac^2-bc^2
=(a+c)(a-c)b-(a+b)(a-b)c-(b+c)(b-c)a
=(a - b) (b - c)(a - c)

Answer 2

2X^4-X^3+2X^2+1
=2X^4-2X^3+2X^2+x^3+1
=2x^2(x^2-x+1)+(x+1)(x^2-x+1)
=(x^2-x+1)(2x^2+x+1)

Answer 3

1)(2*x^2 + x + 1)*(x^2 - x + 1)
2)(x^2 + x - 3)*(x^2 - x + 1)
3)(x^2 + 2*x + 3)*(x^2 - x + 1)
3)(b - c)*(a - c)*(a - b)

Answer 4

2X^4-X^3+2X^2+1=2X^4-2X^3+2X^2+x^3+1=2x^2(x^2-x+1)+(x+1)(x^2-x+1)=(x^2-x+1)(2x^2+x+1)