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

Question
Polynomial arithmetic
asked 2020-10-20
Write the polynomials as the product of linear factors and list all the zeros of the function.\(h(x) = x^{3}-3x^{2}+4x-2\)

Answers (1)

2020-10-21
Step 1 \(x^{3}-3x^{2}+4x-2=0\) Step 2 \(x-1| \frac{x^{2}-2x+2}{x^{3}-3x^{2}+4x-2} \frac{x^{3}-x^{2}}{-2x^{2}+4x-2}|\frac{-2x^{2}+2x}{2x-2}|(2x-2)\) 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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