need help answering

Question

A polynomial P is given.

P(x) = x³ − 3x² + 9x − 27

(a) Factor P into linear and irreducible quadratic factors with real coefficients. 

P(x) = 

Answer 1

You can factor this by grouping the first two terms together and the last two terms together like this:

P(x) = x³ − 3x² + 9x − 27

P(x) = (x³ − 3x²) + (9x − 27)

P(x) = x²(x − 3) + 9(x − 3)

Then by factoring out the common factor "x - 3" like this:

P(x) = (x - 3)(x² + 9)

The linear factor is "x - 3" and the irreducible quadratic factor is "x² + 9"

Answer 2

x³ + 9x - 3x² - 27

x(x² + 9) - 3(x² + 9)

(x - 3)(x² + 9)