Multiply the polynominal expression (x + 2)(x - 4)

Question

?x^2 + ?x + ?

Answer 1

To multiply the polynomial expressions \( (x + 2)(x - 4) \), we can use the distributive property (also known as the FOIL method for binomials):

1. First: Multiply the first terms:
   \( x \cdot x = x^2 \)

2. Outer: Multiply the outer terms:
   \( x \cdot (-4) = -4x \)

3. Inner: Multiply the inner terms:
   \( 2 \cdot x = 2x \)

4. Last: Multiply the last terms:
   \( 2 \cdot (-4) = -8 \)

Now, combine all the results:
\[ x^2 - 4x + 2x - 8 \]

Combine the like terms (\(-4x + 2x\)):
\[ x^2 - 2x - 8 \]

Thus, the final result is:
\[ x^2 - 2x - 8 \]

In summary, the coefficients are:
\(? = 1\),
\(? = -2\),
\(? = -8\)

So the polynomial expression is \( x^2 - 2x - 8 \).

Answer 2

Make it fit the boxes

Answer 3

Sure! Based on the expression we derived from multiplying the polynomials \((x + 2)(x - 4)\), we have:

\[ x^2 - 2x - 8 \]

Now, let's fill in the boxes accordingly:

• For \( x^2 \): 1 (coefficient of \(x^2\))
• For \( x \): -2 (coefficient of \(x\))
• For the constant term: -8

So the answers to fit the boxes would be:

• ? (for \(x^2\)): 1
• ? (for \(x\)): -2
• ? (for the constant term): -8