Question

Factor the polynomial completely.

Answer 1

\[7x ^{3}-4x ^{2}+8x\]

Answer 2

how did you get that? and aren't you supposed to find the 2 numbers after factoring (using the table or box method)

Answer 3

ok

Answer 4

\[7x^3-4x^2+8x=x(7x^2-4x+8)\]
7x^2-4x+8 has no real roots so, to continue factorising, we must use complex numbers.
We solve 7x^2-4x+8 using the quadratic formula to get x = 2/7 +- root(52)/7 i
Thus
\[7x^3-4x^2+8x=x(x- \frac27 - \frac{\sqrt{52}}7 i)(x- \frac27 + \frac{\sqrt{52}}7 i)\]

Answer 5

Which is quite ugly. Stick to the real numbers. It is neater

Answer 6

so what would be the final answer?

Answer 7

Have you worked with complex factorising before?

Answer 8

If not, use the first line of my answer

Answer 9

ok. and no i'm in algebra 2. thanks!

Answer 10

Sure