SOLUTION: Could someone help explain how to properly solve the following? Thank you Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter y

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Could someone help explain how to properly solve the following? Thank you Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter y      Log On


   

Question 1137045: Could someone help explain how to properly solve the following? Thank you
Use the Factor Theorem to find all real zeros for the given polynomial function and one factor. (Enter your answers as a comma-separated list.)
2x^3 + 9x^2 − 12x − 54; 2x + 9
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E3+%2B+9x%5E2+%E2%88%92+12x+%E2%88%92+54
Factor x² out of the first two terms and -12
out of the last two terms:

x%5E2%282x%2B9%5E%22%22%29-6%282x%2B9%5E%22%22%29

Factor (2x+9) out of those two terms:

%282x%2B9%5E%22%22%29%28x%5E2-6%5E%22%22%29

To find the zeros, set that = 0

%282x%2B9%5E%22%22%29%28x%5E2-6%29=0

2x+9=0;   x²-6=0
  2x=-9;    x²=6
 x=-9%2F2   x=%22%22%2B-sqrt%286%29

matrix%281%2C5%2C-9%2F2%2C%22%2C%22%2Csqrt%286%29%2C%22%2C%22%2C-sqrt%286%29%29

Edwin