Answer:
120
Step-by-step explanation:
Before we find the coefficient of the squared term, we need to expand and differentiate the resulting function twice.
Expanding the function:
f(x) = (x² + 4x + 3)(4x³ − 6x² + 8x + 1)
f(x) = 4x^5-6x^4+8x^3+x^2+16x^4-24x^3+32x^2+4x+14x^3-18x^2+24x+3
Collecting the like terms
f(x) = 4x^5+10x^4-2x^3+15x^2+28x+3
Differentiating the resulting function twice, we have;
f'(x) = 20x^4+40x^3-6x^2+30x+28
f''(x) = 80x^3 + 120x^2-12x+30
Based on the second derivative of the function, the coefficient of x² in the function is 120
