Find the coefficient of the $x^2$ term in the expansion of the product $(ax^3 + 3x^2 - 2x)(bx^2 - 7x - 4)$.
I need to multiply the two polynomials and collect like terms to find the coefficient of $x^2$. I can use the distributive property to multiply each term in the first polynomial by each term in the second polynomial. I get $(ax^3 + 3x^2 - 2x)(bx^2 - 7x - 4) = abx^5 - 7ax^4 - 4ax^3 + 3bx^4 - 21x^3 - 12x^2 - 2bx^3 + 14x^2 + 8x$. I can combine like terms by adding the coefficients of the same powers of $x$. I get $abx^5 + (-7a + 3b)x^4 + (-4a - 21 - 2b)x^3 + (14 - 12)x^2 + 8x$. The coefficient of the $x^2$ term is $14 - 12 = 2$. 