Final answer:
To find the coefficient of the x^3 term, we need to expand and combine like terms in the expression (x^2 + 2x + 3)(x^2 - 8x + 4). The coefficient of the x^3 term is -6.
Step-by-step explanation:
To find the coefficient of the x^3 term when (x^2 + 2x + 3)(x^2 - 8x + 4) is simplified, we need to expand the expression. Multiplying the first term (x^2 + 2x + 3) by the second term (x^2 - 8x + 4) gives us:
- (x^2)(x^2) + (x^2)(-8x) + (x^2)(4) + (2x)(x^2) + (2x)(-8x) + (2x)(4) + (3)(x^2) + (3)(-8x) + (3)(4)
- x^4 - 8x^3 + 4x^2 + 2x^3 - 16x^2 + 8x + 3x^2 - 24x + 12
- Combining like terms gives us x^4 - 6x^3 - 5x^2 - 16x + 12
The coefficient of the x^3 term is -6.