Question

Just need a double check of this answer please. Also not sure how to give medals on this thing, that would be helpful I'm sure to those who assist :)

For the polynomial below , -2 is a zero.
g(x)= x^3-4x^2+x+26

Express g(x) as a product of linear factors.

1. x^3-4x^2+x+26 / x+2
2. = x^2-6x+13
3. Using quadratic equation to find the other 2 zeros
4. X= (3+2i) and (3-2i)
5. Factored into products of linear factors:
g(x)= (x+2)(x-3-2i)(x-3+2i)

Answer 1

x^3-4x^2+x+26
0 -2 12 -26
----------------
-2 | 1x^2 -6x+ 13

thats looking good so far

Answer 2

and yes, to get it into a product of linear factors, you would have to use complex values

Answer 3

x^2 -6x + 9 = -13 + 9

(x-3)^2 = -4

x = +- sqrt(-4) + 3

Answer 4

\[(x-3-\sqrt{-4}) (x-3+\sqrt{-4})\]

Answer 5

Since it has a complex value I can't use integers. So I have to find the other two zeros using the quadratic equation. That's how I found (x-3+/-2i). isn't the imaginary (2i) the same thing as square rt 4?

Answer 6

yes it is

Answer 7

Also isn't -2 a factor of g(x)?

Answer 8

it is, i was focusing more on the imaginary parts :)

Answer 9

Just want to be sure before I tap it out as an answer:
g(x)= (x+2)(x−3−squart−4)(x−3+squart-4)

Answer 10

gotcha.

Answer 11

just verifying that (x+2) is supposed to go in there at the beginning.

Answer 12

your work looks good to me :)

Answer 13

Thanks again amistre! As always you're a pro!! How do I do the medal thing on here? lol

Answer 14

there whould be a blue "best response" button on the right side of every post. Thats the "give medal" button.

if you dont see the button, try to refresh your browser with an f5, used to do the trick

Answer 15

Got it! Thank you

Answer 16

good luck ;)