How do you factor given that $f (- 14) = 0$ $f(-14)=0$ and $f (x) = x^{3} + 11 x^{2} - 150 x - 1512$ $f(x)=x^3+11x^2-150x-1512$ ?

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How do you factor given that $f (- 14) = 0$ $f(-14)=0$ and $f (x) = x^{3} + 11 x^{2} - 150 x - 1512$ $f(x)=x^3+11x^2-150x-1512$ ?

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Answer 1 · 2016-10-05T20:20:07

$(x - 12) (x + 9) (x + 14)$ $(x-12)(x+9)(x+14)$

Explanation:

When you know that $f (c) = 0$ $f(c)=0$ for some value $c$ $c$ , you knot that $f (x)$ $f(x)$ has a factor $(x - c)$ $(x-c)$ . So, you can divide $x^{3} + 11 x^{2} - 150 x - 1512$ $x^3+11x^2-150x-1512$ by $(x + 14)$ $(x+14)$ via long division, or whatever method you prefer, and obtain

$\frac{x^{3} + 11 x^{2} - 150 x - 1512}{x + 14} = x^{2} - 3 x - 108$ $(x^3+11x^2-150x-1512)/(x+14) = x^2-3 x-108$

which means

$(x^{2} - 3 x - 108) (x + 14) = x^{3} + 11 x^{2} - 150 x - 1512$ $(x^2-3 x-108)(x+14) = x^3+11x^2-150x-1512$

Again, $x^{2} - 3 x - 108$ $x^2-3 x-108$ has solutions $12$ $12$ and $- 9$ $-9$ , which means that it can be written as $(x - 12) (x + 9)$ $(x-12)(x+9)$

Thus, we can write

$x^{3} + 11 x^{2} - 150 x - 1512 = (x^{2} - 3 x - 108) (x + 14) = (x - 12) (x + 9) (x + 14)$ $x^3+11x^2-150x-1512 = (x^2-3 x-108)(x+14) = (x-12)(x+9)(x+14)$

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How do you factor given that $f (- 14) = 0$ $f(-14)=0$ and $f (x) = x^{3} + 11 x^{2} - 150 x - 1512$ $f(x)=x^3+11x^2-150x-1512$ ?

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Explanation:

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How do you factor given that f(−14)=0f(-14)=0 and f(x)=x3+11x2−150x−1512f(x)=x^3+11x^2-150x-1512?

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Explanation:

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How do you factor given that $f (- 14) = 0$ $f(-14)=0$ and $f (x) = x^{3} + 11 x^{2} - 150 x - 1512$ $f(x)=x^3+11x^2-150x-1512$ ?