# Math Help - Solving a cubic equation.

1. ## Solving a cubic equation.

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

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

2. By guessing one root...

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

3. Assuming you know the factor theorem
the numbers are big,
so arrangement could help

so when x=3 , it satisfies the equation, (x-3) is a factor, and other factors can be found by equating coefficients.

4. 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.
\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.

5. THANK YOU ALL SO MUCH! This is very helpful!