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# Trace the curve of x^3 - 6x^2 +11x - y = 6 # Trace the curve of x^3 - 6x^2 +11x - y = 6

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Analytic geometry asked 2021-01-31
Trace the curve of $$\displaystyle{x}^{{3}}-{6}{x}^{{2}}+{11}{x}-{y}={6}$$

## Answers (1) 2021-02-01
$$\displaystyle{x}^{{3}}-{6}{x}^{{2}}+{11}{x}-{y}={6}$$
$$\displaystyle{y}={x}^{{3}}-{6}{x}^{{2}}+{11}{x}-{6}$$
$$\displaystyle{p}{\left({x}\right)}={x}^{{3}}-{6}{x}^{{2}}+{11}{x}-{6}$$
$$\displaystyle{p}{\left({1}\right)}={1}-{6}+{11}-{6}={0}$$
(x-1) is a point of p(x)
Dividing p(x) by (x-2) we get
$$\displaystyle{q}{\left({x}\right)}={x}^{{2}}-{3}{x}-{21}{x}+{6}$$
$$\displaystyle{q}{\left({x}\right)}={x}{\left({x}-{3}\right)}-{2}{\left({x}-{3}\right)}$$
$$\displaystyle{q}{\left({x}\right)}={\left({x}-{2}\right)}{\left({x}-{3}\right)}$$
$$\displaystyle{p}{\left({x}\right)}={\left({x}-{1}\right)}{q}{\left({x}\right)}$$
$$\displaystyle{p}{\left({x}\right)}={\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{3}\right)}$$
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