Factor x4 - 3x3 - 7x2 plus 27x -18?

Answer 1

First, it is important to regroup, so I am going to rearrange this equation:

(x4 - 7x2 - 18 - 3x3 + 27x

I can now factor the first three terms and the last two terms:

(x4 - 7x2 - 18) becomes (x2 - 9)(x2 + 2)

-3x3 + 27x becomes -3x(x2 - 9); so the new equation looks like:

(x2 - 9)(x2 + 2) - 3x(x2 - 9)

From here, factor out what is common, in this case- x2- 9. Therefore, you will have

(x2 - 9)(x2 + 2 - 3x), which can be rearranged to (x2 -9)(x2 - 3x + 2).

Further factoring reveals

(x + 3)(x - 3)(x - 1)(x - 2) as the final answer.