Answer:
(c) -42
Explanation:
You want the product ab given that ...
- f(x) = 3x³ +ax² -5x +7
- g(x) = -3x⁴ +2x³ +3x² +bx +12
- (f+g)(x) = -3x⁴ +5x³ +9x² -12x +19
Comparing coefficients
The function (f+g)(x) is the sum of the other two functions. For the purpose here, we only need to look at terms that involve 'a' and 'b'.
Comparing coefficients of x², we have ...
ax² +3x² = 9x²
a = 9 -3 = 6
Comparing coefficients of x, we have ...
-5x +bx = -12x
b = -12 +5 = -7
The product is ...
ab = (6)(-7) = -42