To find the middle term in the product \((x+3)(x-4)\), we need to perform polynomial multiplication.
Step-by-step, we multiply each term in the first polynomial by each term in the second polynomial:
1. Multiply \(x\) by \(x\):
[tex]\[
x \cdot x = x^2
\][/tex]
2. Multiply \(x\) by \(-4\):
[tex]\[
x \cdot (-4) = -4x
\][/tex]
3. Multiply \(3\) by \(x\):
[tex]\[
3 \cdot x = 3x
\][/tex]
4. Multiply \(3\) by \(-4\):
[tex]\[
3 \cdot (-4) = -12
\][/tex]
Now, we sum all these products together to get the expanded form of the polynomial:
[tex]\[
x^2 - 4x + 3x - 12
\][/tex]
Next, we combine like terms (specifically the \(x\) terms):
[tex]\[
-4x + 3x = -x
\][/tex]
So, the final expanded polynomial is:
[tex]\[
x^2 - x - 12
\][/tex]
The middle term of this polynomial is the term with the coefficient of \(x\). Thus, the middle term is:
[tex]\[
-x
\][/tex]
Hence, the answer is [tex]\(-x\)[/tex].
