 # Write the polynomials as the product of linear factors and list all the zeros of the function.h(x) = x^{3}-3x^{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.$h\left(x\right)={x}^{3}-3{x}^{2}+4x-2$
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Step 1 ${x}^{3}-3{x}^{2}+4x-2=0$ Step 2 $x-1|\frac{{x}^{2}-2x+2}{{x}^{3}-3{x}^{2}+4x-2}\frac{{x}^{3}-{x}^{2}}{-2{x}^{2}+4x-2}|\frac{-2{x}^{2}+2x}{2x-2}|\left(2x-2\right)$ Step 3 $x-1|\frac{{x}^{2}-2x+2}{x-1}\left({x}^{2}-2x+2\right)=0$
$x=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$
$x=\frac{-\left(-2\right)±\sqrt{\left(-2{\right)}^{2}-4\left(1\right)\left(2\right)}}{2\left(1\right)}$
$x=1.1±i$
$f\left(x\right)=\left(x-\left(1+i\right)\right)\left(x-\left(1-i\right)\right)\left(x-1\right)$