Can anyone help me solve this? Thank you so so much!

16x^3 -48x^2 -9x + 27=0

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- Jul 4th 2010, 11:53 AMjulia78Solving a cubic equation.
Can anyone help me solve this? Thank you so so much!

16x^3 -48x^2 -9x + 27=0 - Jul 4th 2010, 12:27 PMAlso sprach Zarathustra
By guessing one root...

My "guess" is x=3, now you should know how to continue.

Read here please: Rational Zeros of Polynomials - Jul 4th 2010, 12:32 PMzeeshahmad
Assuming you know the factor theorem

the numbers are big,

so arrangement could help

Attachment 18096

so when x=3 , it satisfies the equation, (x-3) is a factor, and other factors can be found by equating coefficients. - Jul 4th 2010, 12:43 PMeumyang
This cubic can be factored by grouping. Look at the first pair of terms and factor out the GCF; then do the same for the last pair.

$\displaystyle \begin{aligned}

16x^3 - 48x^2 - 9x + 27 &= 0 \\

16x^2(x - 3) - 9(x - 3) &= 0\\

(x - 3)(16x^2 -9) &= 0

\end{aligned}

$

Can you take it from here? Finish factoring (look at 16x^2 - 9), and set each factor equal to 0. - Jul 6th 2010, 01:55 PMjulia78
THANK YOU ALL SO MUCH! This is very helpful!