Write the polynomials as the product of linear factors and list all the zeros of the function.$h(x)={x}^{3}-3{x}^{2}+4x-2$

CheemnCatelvew
2020-10-20
Answered

Write the polynomials as the product of linear factors and list all the zeros of the function.$h(x)={x}^{3}-3{x}^{2}+4x-2$

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sweererlirumeX

Answered 2020-10-21
Author has **91** answers

Step 1
${x}^{3}-3{x}^{2}+4x-2=0$
Step 2
$x-1|\frac{{x}^{2}-2x+2}{{x}^{3}-3{x}^{2}+4x-2}\frac{{x}^{3}-{x}^{2}}{-2{x}^{2}+4x-2}|\frac{-2{x}^{2}+2x}{2x-2}|(2x-2)$
Step 3
$x-1|\frac{{x}^{2}-2x+2}{x-1}({x}^{2}-2x+2)=0$

$x=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}$

$x=\frac{-(-2)\pm \sqrt{(-2{)}^{2}-4(1)(2)}}{2(1)}$

$x=1.1\pm i$

$f(x)=(x-(1+i))(x-(1-i))(x-1)$

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