How do you factor given that $f(10)=0$ and $f(x)=x^3-12x^2+12x+80$ ?

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Answer 1 · 2016-12-19T08:13:23

$f(x)=x^3-12x^2+12x+80=(x-10)(x+2)(x-4)$

As $f(x)=x^3-12x^2+12x+80$ and $f(10)=0$

$(x-10)$ is a factor of $f(x)=x^3-12x^2+12x+80$

Now dividing $f(x)=x^3-12x^2+12x+80$ by (x-10)#, we can get a quadratic polynomial which can be factorized further by splitting the middle term.

$f(x)=x^3-12x^2+12x+80$

= $x^2(x-10)-2x(x-10)-8(x-10)$

= $(x-10)(x^2-2x-8)$

= $(x-10)(x^2-4x+2x-8)$

= $(x-10)(x(x-4)+2(x-4))$

= $(x-10)(x+2)(x-4)$

How do you factor given that f(10)=0f(10)=0 and f(x)=x^3-12x^2+12x+80f(x)=x^3-12x^2+12x+80?