Respuesta :
Answer:
x³ - 19x - 12
Step-by-step explanation:
complex roots occur as conjugate pairs
2 + [tex]\sqrt{7}[/tex] is a root then 2 - [tex]\sqrt{7}[/tex] is also a root
hence the factors of the polynomial are
(x + 4), (x - (2 + [tex]\sqrt{7}[/tex]) )(x - (2 - [tex]\sqrt{7}[/tex]))
and f(x) = (x + 4)(x - 2 - [tex]\sqrt{7}[/tex])(x - 2 + [tex]\sqrt{7}[/tex])
= (x + 4)((x - 2)² - ([tex]\sqrt{7}[/tex])²)
= (x + 4)(x² - 4x + 4 - 7)
= (x + 4)(x² - 4x - 3)
= x³ - 4x² - 3x + 4x² - 16x - 12 ← collect like terms
= x³ - 19x - 12
