請問x⁴-2x³+9x²-8x+16利用因式分解如何算?
回答 (2)
2016-11-15 12:07 am
=x^3(x-2)+9x^2-8(x-2)
=(x^3-8)(x-2)+9x^2
=(x-2)(x^2+2x+4)(x-2)+9x^2
=((x-2)^2-(-3x)^2)(x^2+2x+4)
=-(x+2+3x)(x+2-3x)(x^2+2x+4)
=(x^3-8)(x-2)+9x^2
=(x-2)(x^2+2x+4)(x-2)+9x^2
=((x-2)^2-(-3x)^2)(x^2+2x+4)
=-(x+2+3x)(x+2-3x)(x^2+2x+4)
2016-10-22 1:27 pm
Sol
x^4－2x^3+9x^2－8x+16
=(x^4－x^3+4x^2)+( －^3+x^2－4x)+(4x^2－4x+16)
=x^2(x^2－x+4)-x(x^2－x+4)+4(x^2－x+4)
=(x^2－x+4)(x^2－x+4)
=(x^2－x+4)^2
x^4－2x^3+9x^2－8x+16
=(x^4－x^3+4x^2)+( －^3+x^2－4x)+(4x^2－4x+16)
=x^2(x^2－x+4)-x(x^2－x+4)+4(x^2－x+4)
=(x^2－x+4)(x^2－x+4)
=(x^2－x+4)^2
收錄日期: 2021-04-18 15:44:52
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20161022044043AA19ojV