Final answer:
The middle term in the quadratic function (x-4)(3x+2) is found by multiplying the terms and combining like terms, resulting in the middle term -10x.
Step-by-step explanation:
To find the middle term in the quadratic function given by the product of binomials (x-4)(3x+2), we need to perform multiplication. Notice that a quadratic function is in the general form at² + bt + c = 0, where 'b' represents the coefficient of the middle term. In our case, the multiplication process goes like this:
- x multiplied by 3x gives 3x² (This is the 'a' term).
- x multiplied by 2 gives 2x (First part of the middle term).
- -4 multiplied by 3x gives -12x (Second part of the 'b' term).
- -4 multiplied by 2 gives -8 (This is the 'c' term).
Add the two parts of the middle term together (2x and -12x) to get -10x. Thus, the middle term of the given quadratic function is -10x.