Question

15 POINTS!!!!! !!!!!! could i have some help on #39 with an explanation?? i just really don’t get it, lol. i thought i did, but then i looked at the answer key, and it is NOT what i thought. thank you guys so much, and happy halloween!!

Answer 1

Hey there! In this problem, the solutions, both real and imaginary are provided. We have to work backwards to create a polynomial function which matches these solutions:

f(x) = (x - 6), (x + [5 + 2i]), (x + [5 - 2i])

Create a difference of squares,

f(x) = (x - 6), ([x + 5] + 2i), ([x + 5] - 2i)

f(x) = (x - 6), ([x + 5]^2 + 4)

[(x + 5)(x + 5)] + 4

x^2 + 5x + 5x + 25 + 4

x^2 + 10x + 29

f(x) = (x-6), (x^2 + 10x + 29)

f(x) = x^3 + 10x^2 + 29x - 6x^2 - 60x - 174

Combine like terms,

f(x) = x^3 + 4x^2 + 29x - 174

There we have our answer, a polynomial of degree 3.

$f(x) = x^3 + 4x^2 + 29x - 174$