Question

把下列格式分解因式,(1)x^4+64(2)x^3-11x^2+31x-21

Answer 1

x^4+64=X^4+64+16X^2-16X^2

=(X^2+8)-16X^2

=(X^2+8-4X)(X^2+8+4X)

x^3-11x^2+31x-2

=(x³-1)-(11x³-31x+20)

=(x-1)(x²+x+1)-(11x-20)(x-1)

=(x-1)(x²+x+1-11x+20)

=(x-1)(x²-10x+21)

=(x-1)(x-3)(x-7)