Question

把下列各式分解因式

4x³-31x+15= (2)X^5+X+1 (3)2a^4-a^3-6a²-a+2 (4)x^3+5x²+3x-9 (5)2a²b²+2a²c²+2b²c²-a^4-b^4-c^4

Answer 1

①4x³-31x+15
=4x^3-x-30x+15
=x(2x+1)(2x-1)-15(2x-1)
=(2x-1)(2x^2+x-15)
=(2x-1)(2x-5)(x+3)
②X^5+X+1
=(x^5-x^2)+x^2+x+1
=x^2(x-1)(x^2+x+1)+(x^2+x+1)
=(x^2+x+1)(x^3-x^2+1)
③2a^4-a^3-6a²-a+2
=a^3(2a-1)-(2a-1)(3a+2)
=(2a-1)(a^3-3a-2)
=(2a-1)(a^3+a^2-a^2-a-2a-2)
=(2a-1)(a+1)(a^2-a-2)
=(2a-1)(a-2)(a+1)^2
④x^3+5x²+3x-9
=x^3-x^2+6x^2-6x+9x-9
=(x-1)(x^2+6x+9)
=(x-1)(x+3)^2
⑤2a²b²+2a²c²+2b²c²-a^4-b^4-c^4
=4a²b²-(a^2+b^2-c^2)^2
=(2ab+a^2+b^2-c^2)(2ab-a^2-b^2+c^2)
=-(a+b+c)(a+b-c)(a-b+c)(a-b-c)