Multiply the polynomial expression (x+2)(x−4). (2 points)

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. Multiply the first terms: \[ x \cdot x = x^2 \]

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

3. Multiply the inner terms: \[ 2 \cdot x = 2x \]

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

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

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

So, the completed expression is: \[ x^2 - 2x - 8 \]

Thus, filling in the blanks, we have: \[ x^2 + (-2)x + (-8) \]

So the answer is:

• The coefficient of \( x \) is \(-2\).
• The constant term is \(-8\).

Final answer: \[ x^2 + (-2)x + (-8) \]

Answer 2

Multiply the polynomial expression (x+2)(x−4). (2 points)
___x^2+___x+___

Answer 3

To multiply the polynomial expressions \((x + 2)(x - 4)\), we can use the distributive property (or FOIL method). Let's perform the multiplication step by step:

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

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

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

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

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

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

Now, write it in the form \(Ax^2 + Bx + C\): \[ 1x^2 + (-2)x + (-8) \]

So, the completed expression is:

• The coefficient of \(x^2\) is \(1\).
• The coefficient of \(x\) is \(-2\).
• The constant term is \(-8\).

Final answer: \[ 1x^2 + (-2)x + (-8) \]

In terms of filling in the blanks:

• First blank (for \(x^2\)): 1
• Second blank (for \(x\)): -2
• Third blank (constant): -8

So, the overall completed expression in the format \(___x^2 + ___x + ___\) is: 1, -2, -8.