Multiply: [tex](x+3)(x-4)[/tex]

What is the middle term in the simplified product?

A. [tex]x[/tex]

B. [tex]-x[/tex]

C. [tex]3x[/tex]

D. [tex]-4x[/tex]



Answer :

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].