How do you use the graph of $f (x) = x^{3} - 6 x^{2} + 11 x - 6$ $f(x) =x^3-6x^2+11x-6$ to rewrite $f (x)$ $f(x)$ as a product of linear factors?

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How do you use the graph of $f (x) = x^{3} - 6 x^{2} + 11 x - 6$ $f(x) =x^3-6x^2+11x-6$ to rewrite $f (x)$ $f(x)$ as a product of linear factors?

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Answer 1 · 2017-03-26T11:54:40

$f (x) = (x - 1) (x - 2) (x - 3)$ $f(x)=color(green)((x-1)(x-2)(x-3))$

Explanation:

Here is the graph of $f (x) = x^{3} - 6 x^{2} + 11 x - 6$ $f(x)=x^3-6x^2+11x-6$
enter image source here
Notice that the graph crosses the X-axis at three points.

$f (x) = 0$ $f(x)=0$ when :
$XXX x = 1 XX \to XX (x - 1)$ $color(white)("XXX")x=1color(white)("XX")rarrcolor(white)("XX")(x-1)$ is a factor of $f (x)$ $f(x)$
$XXX x = 2 XX \to XX (x - 2)$ $color(white)("XXX")x=2color(white)("XX")rarrcolor(white)("XX")(x-2)$ is a factor of $f (x)$ $f(x)$
$XXX x = 3 XX \to XX (x - 3)$ $color(white)("XXX")x=3color(white)("XX")rarrcolor(white)("XX")(x-3)$ is a factor of $f (x)$ $f(x)$

Since $f (x)$ $f(x)$ is of degree $3$ $3$ it has a maximum of $3$ $3$ factors,
so these $3$ $3$ represent a complete factoring of $f (x)$ $f(x)$ .

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How do you use the graph of $f (x) = x^{3} - 6 x^{2} + 11 x - 6$ $f(x) =x^3-6x^2+11x-6$ to rewrite $f (x)$ $f(x)$ as a product of linear factors?

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Explanation:

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How do you use the graph of f(x)=x3−6x2+11x−6f(x) =x^3-6x^2+11x-6 to rewrite f(x)f(x) as a product of linear factors?

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How do you use the graph of $f (x) = x^{3} - 6 x^{2} + 11 x - 6$ $f(x) =x^3-6x^2+11x-6$ to rewrite $f (x)$ $f(x)$ as a product of linear factors?