Question

factor 324= x^3-12x^2+27x-324 PLEASE HELP

Answer 1

0 = x^3 - 12x^2 + 27x - 324
flip the second and third terms
0 = x^3 + 27x - 12x^2 - 324
group the first two terms and the last two terms
0 = (x^3 + 27x) - (12x^2 + 324)
factor out common terms
0 = x(x^2 + 27) - 12(x^2 + 27)
apply the Distributive Property
0 = (x - 12)(x^2 + 27)
We have two factors.
Set each equal to zero and solve for x.
x - 12 = 0
x = +12

x^2 + 27 = 0
x^2 = -27
x = √(-27)
x = √(-1) * √(27)
x = i * √(9 * 3)
x = i * (+-3√3)
x = -3i√3 and +3i√3

So the three solutions are
+12 and -3i√3 and +3i√3

Im not sure if this is the right answer, but you can check it.. LOL

Answer 2

@Trexy I think you missed the 324 at the beginning of the question.

Answer 3

ooh well.. Sorry about that..lol Can you check it @Calcmathlete ??

Answer 4

lol. I did it in my head and factoring by grouping doesn't work so well...you'd have to go through rational root theorem, descartes rule of signs, etc and it's well...meh...

Answer 5

i did all of that i just need to factor it

Answer 6

Thank You for Correcting it @Calcmathlete XD

Answer 7

np

Answer 8

Can any one please help Find the solutions to this equation algebraically using the Fundamental Theorem of Algebra, the Rational Root Theorem, Descartes' Rule of Signs, and the Factor Theorem. I did everything except the factor part what do I need to do

Answer 9

It does not factor if there is a 324 on the LHS

Answer 10

Here are the roots that Mathematica gave
\[
\begin{array}{c}
x=4+\frac{1}{3} \sqrt[3]{9018-243
\sqrt{1373}}+\sqrt[3]{334+9 \sqrt{1373}} \\
x=4-\frac{1}{6} \left(1+i \sqrt{3}\right)
\sqrt[3]{9018-243 \sqrt{1373}}-\frac{1}{2}
\left(1-i \sqrt{3}\right) \sqrt[3]{334+9
\sqrt{1373}} \\
x=4-\frac{1}{6} \left(1-i \sqrt{3}\right)
\sqrt[3]{9018-243 \sqrt{1373}}-\frac{1}{2}
\left(1+i \sqrt{3}\right) \sqrt[3]{334+9
\sqrt{1373}} \\
\end{array}

\]

Answer 11

It does not have rational roots. Does it really have a 324 on the LHS?

Answer 12

Did you type your equation right?

Answer 13

yes

Answer 14

so you can't factor it?

Answer 15

Not with rational numbers.

Answer 16

I think the 324 on the LHS must be zero. In the case, one of the posts above
solved it for you.