Question

F(x) = x4 - x3 - 2x- 4 factor the polynomial function over the complex numbers

Answer 1

(x+1)(x-2)(x+i
`√(2)`) (x-i
`√(2)`)

Explanation:

I took the test on K12 and got it right.

Answer 2

f(x) = = (x + √2 i) (x - √2 i) (x - 2 ) (x + 1)

Explanation:

The given function is f(x) = x⁴ - x³ -2x -4

factor the polynomial function

f(x) = x⁴ - x³ -2x -4 = (x⁴ - 4) - (x³ + 2x ) ⇒ take (-) as a common from (- x³ -2x)

= (x² + 2 ) (x² - 2) - x (x² + 2) ⇒ take (x² + 2) as a common

= (x² + 2 ) ( x² - x - 2)

= (x + √2 i) (x - √2 i) (x -2 ) ( x+1)

Notes: (x⁴ - 4) = (x² + 2 ) (x² - 2)

(x² + 2)= (x + √2 i) (x - √2 i)

( x² - x - 2) = (x -2 ) ( x+1)