Question

因式分解4题

x^3-5x+4
a^2-4ab+3b^2+2bc-c^2
x^3-4x^2+5x-6
x^4+2x^2-2a-a^2

Answer 1

x^3-5x+4
=x^3-x^2+x^2-x-4x+4
=x^2(x-1)+x(x-1)-4(x-1)
=(x-1)(x^2+x-4)

a^2-4ab+3b^2+2bc-c^2
=a^2-4ab+4b^2-b^2+2bc-c^2
=(a-2b)^2-(b-c)^2
=(a-2b+b-c)(a-2b-b+c)
=(a-b-c)(a-3b+c)

x^3-4x^2+5x-6
=x^3-3x^2-x^2+5x-6
=x^2(x-3)-(x-2)(x-3)
=(x-3)(x^2-x+2)

x^4+2x^2-2a-a^2
=x^4+2x^2+1-1-2a-a^2
=(x^2+1)^2-(a+1)^2
=(x^2+1+a+1)(x^2+1-a-1)
=(x^2+a+2)(x^2-a)

Answer 2

x^3-5x+4
=x^3-x^2+x^2-x-4x+4
=x^2*(x-1)+x*(x-1)-4*(x-1)
=(x^2+x-4)(x-1)