SOLUTION: Which of the following expressions is equal to -3x^2-27 A ) (-3x-3i)(x-9i) B ) (-3x-9i)(x+3i) C ) (-3x+3i)(x+9i) D ) (-3X+9i)(x+3i) i know i have to factor (i think) to solve

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Which of the following expressions is equal to -3x^2-27 A ) (-3x-3i)(x-9i) B ) (-3x-9i)(x+3i) C ) (-3x+3i)(x+9i) D ) (-3X+9i)(x+3i) i know i have to factor (i think) to solve       Log On


   



Question 1082119: Which of the following expressions is equal to -3x^2-27
A ) (-3x-3i)(x-9i)
B ) (-3x-9i)(x+3i)
C ) (-3x+3i)(x+9i)
D ) (-3X+9i)(x+3i)
i know i have to factor (i think) to solve it but i'm having trouble when it comes to getting the final form ( cant think of the right term)

Found 3 solutions by Boreal, math_helper, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
it is -3(x^2+9)=or -3(x+/-3i)=-3(x+3i)(x-3i)
-3x+9i could be one factor with (x+3i), -3x-9i could be another with (x-3i).
D works.
-3(x-3i)(x+3i)

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Three criteria must be met:
1) the factors must multiply to give a -3x^2 terms (all of therm do)
2) the factors must multiply such that the xi terms cancel (NOT all of them do)
3) the factors must multiply to give -27 (= +27i^2 because i^2 = -1) (NOT all of them do)
I'll add that A) is NOT correct because +%28-3x-3i%29%28x-9i%29+=+-3x%5E2+-3xi+%2B+27xi+%2B27i%5E2+ —> which has a +24xi term.


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D: +%28-3x%2B9i%29%28x%2B3i%29+=+-3x%5E2+-+9xi+%2B+9xi+%2B+27i%5E2++=+-3x%5E2+-+27+

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

-3x%5E2-27
-3%28x%5E2%2B9%29
-3%28x%5E2%2B3%5E2%29........here we have the sum of squares %28x%5E2%2B3%5E2%29 and we can write it as the difference of squares if we write 3%5E2 as -3%5E2%28-1%29, and we know that -1=i%5E2; so, we have %28x%5E2-3%5E2i%5E2%29 or
%28x%5E2-%283i%29%5E2%29 now factor it as the difference of the squares and you have x%5E2%2B9=%28x+-3i%29+%28x+%2B+3i%29
plug it in:
-3%28x+-3i%29%28x+%2B+3i%29....multiply -3%28x+-3i%29
%28-3x+-%28-3%293i%29%28x+%2B+3i%29
%28-3x+%2B9i%29%28x+%2B+3i%29
answer:
D ) %28-3X%2B9i%29%28x%2B3i%29