Final answer:
To find the function q(a), we used the information given about p(a) and (p - q)(a). After rearranging the equation and combining like terms, we determined that q(a) = -8a^2 + a + 1.
Step-by-step explanation:
The student has provided two functions, p(a) and q(a), with p(a) being defined as 3a - 5a^2 and the difference between these functions, (p - q), being defined as 3a^2 + 2a - 1. To find q(a), we need to solve for q using the given equations.
First, let's rewrite the equation in the form p(a) - q(a) = (p - q)(a):
3a - 5a^2 - q(a) = 3a^2 + 2a - 1
Then, we move q(a) to the right side and the terms of (p - q)(a) to the left side:
q(a) = -3a^2 + 3a - 5a^2 - (3a^2 + 2a - 1)
Combining like terms, we get:
q(a) = -3a^2 + 3a - 5a^2 - 3a^2 - 2a + 1
Finally, we simplify to find q(a):
q(a) = -8a^2 + a + 1