Use the Distributive Property to rewrite the polynomial (x+8)(x−2)

Question

.(2 points)
__x^2+___x+____

Answer 1

To use the Distributive Property (also known as the FOIL method for binomials) to rewrite the polynomial \((x + 8)(x - 2)\), we can follow these steps:

1. First: Multiply the first terms: \(x \cdot x = x^2\)
2. Outer: Multiply the outer terms: \(x \cdot (-2) = -2x\)
3. Inner: Multiply the inner terms: \(8 \cdot x = 8x\)
4. Last: Multiply the last terms: \(8 \cdot (-2) = -16\)

Now, combine all these results:

\[ x^2 - 2x + 8x - 16 \]

Combine like terms \(-2x\) and \(8x\):

\[ x^2 + 6x - 16 \]

So, the polynomial \((x + 8)(x - 2)\) rewritten using the Distributive Property is:

\[ x^2 + 6x - 16 \]

Now, filling in the blanks:

• First blank: \(1\) (coefficient of \(x^2\))
• Second blank: \(6\) (coefficient of \(x\))
• Third blank: \(-16\) (constant term)

Final answer:

\(x^2 + 6x - 16\)

So, the filled-in equation is:

__x^2+6x+ (-16)