How do you factor given that $f (- 5) = 0$ $f(-5)=0$ and $f (x) = 4 x^{3} + 9 x^{2} - 52 x + 15$ $f(x)=4x^3+9x^2-52x+15$ ?

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Answer 1 · 2016-11-17T21:36:48

We know that $- 5$ $-5$ is a factor by the remainder theorem. We divide $4 x^{3} + 9 x^{2} - 52 x + 15$ $4x^3 + 9x^2 - 52x + 15$ by $x + 5$ $x + 5$ :

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So, our current factoring is $(x + 5) (4 x^{2} - 11 x + 3)$ $(x + 5)(4x^2 - 11x + 3)$ .

$4 x^{2} - 11 x + 3$ $4x^2 - 11x + 3$ cannot be factored any further, so this is as far as we can go.

Hopefully this helps!

How do you factor given that f(−5)=0f(-5)=0 and f(x)=4x3+9x2−52x+15f(x)=4x^3+9x^2-52x+15?