Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -4, 2+(root 7) i know the answer is a trinomial because it makes sense 2+/- (root 7) but i need doing it .

x³ - 19x - 12

Step-by-step explanation:

complex roots occur as conjugate pairs

2 + is a root then 2 - is also a root

hence the factors of the polynomial are

(x + 4), (x - (2 + ) )(x - (2 - ))

and f(x) = (x + 4)(x - 2 - )(x - 2 + )

            = (x + 4)((x - 2)² - ()²)

            = (x + 4)(x² - 4x + 4 - 7)

            = (x + 4)(x² - 4x - 3)

            = x³ - 4x² - 3x + 4x² - 16x - 12 ← collect like terms

            = x³ - 19x - 12

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above