Answer:
A. -6
Step-by-step explanation:
Simplify the given expression.
(6x^4 - 3x^2) + (x^2 - 5)(qx^2 + 5) =
= 6x^4 - 3x^2 + qx^4 + 5x^2 - 5qx^2 - 25
= 6x^4 + qx^4 + 2x^2 - 5qx^2 - 25
= (6 + q)x^4 + (2 - 5q)x^2 - 25
Set ti equal to the given solution.
(6 + q)x^4 + (2 - 5q)x^2 - 25 = 32x^2 - 25
The solution has no 4th degree term, so
6 + q = 0
q = -6
As a check, the solution's x^2 term is 32x^2, so
(2 - 5q)x^2 = 32x^2
2 - 5q = 32
-5q = 30
q = -6
Once again, we get q = -6.
Answer: A. -6
