Factor 4x^3 - 9x^2 + 6x + 1?

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Factor 4x^3 - 9x^2 + 6x + 1?

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Answer 1 · 2017-05-12T04:34:36

$f(x)=4x^3-9x^2+6x+1$ does not have rational factors.

Explanation:

If $(x-a)$ is a factor of $f(x)=4x^3-9x^2+6x+1$ , $a$ could be a factor of $+-1/4$ - here $1$ comes from constant term and $4$ comes from the coefficient of highest power $x^3$ .

Hence, $a$ could be $+-1/4$ , $+-1/2$ or $+-1$ .

Further from factor theorem if $(x-a)$ is a factor of $f(x)$ then $f(a)=0$ .

We know here that $f(1)=2$ and $f(-1)=-18$ and hence $(x-1)$ and $(x+1)$ are not the factors of $f(x)$ . Similarly

$f(1/2)=4/8-9/4+3+1!=0$ and $f(-1/2)=-4/8+9/4-3+1!=0$

$f(1/4)=4/64-9/16+3/4+1!=0$ and $f(-1/4)=-4/64-9/16-3/4+1!=0$

Hence $f(x)=4x^3-9x^2+6x+1$ does not have rational factors.

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Factor 4x^3 - 9x^2 + 6x + 1?

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