To multiply the polynomial expression \((x + 2)(x - 4)\), we can use the distributive property (commonly known as the FOIL method for binomials):
\[ (x + 2)(x - 4) = x \cdot x + x \cdot (-4) + 2 \cdot x + 2 \cdot (-4) \]
Calculating each term, we get:
- \(x \cdot x = x^2\)
- \(x \cdot (-4) = -4x\)
- \(2 \cdot x = 2x\)
- \(2 \cdot (-4) = -8\)
Now, combining these results:
\[ x^2 - 4x + 2x - 8 \]
Combine the like terms:
\[ x^2 + (-4x + 2x) - 8 = x^2 - 2x - 8 \]
So, the final expression is:
\[ x^2 - 2x - 8 \]
Now we can fill in the blanks:
- For \(x^2\), the coefficient is 1.
- For \(x\), the coefficient is -2.
- The constant term is -8.
Thus, the answer is:
1 x^2 + (-2) x + (-8).
1 answer