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

Question

.(2 points)
x2+
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. Next, multiply the outer terms:
   \(x \cdot (-4) = -4x\)

3. Then, multiply the inner terms:
   \(2 \cdot x = 2x\)

4. Finally, multiply the last terms:
   \(2 \cdot (-4) = -8\)

Now, combine all of these results together:

\[ x^2 - 4x + 2x - 8 \]

Now, combine the like terms \(-4x\) and \(2x\):

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

So, the final result of multiplying the polynomials \((x + 2)(x - 4)\) is:

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

Therefore, filling in the blanks from your question:

\[ x^2 + x + \text{(not applicable, -2x)} - 8 \]

The expression is \(x^2 - 2x - 8\).

Answer 2

Multiply to simplify the polynomial expression (r−1)(r2−2r+3)
.(2 points)
r3+
r2+
r+

Answer 3

To multiply and simplify the polynomial expression \((r - 1)(r^2 - 2r + 3)\), you can distribute each term in the first polynomial by each term in the second polynomial.

1. Multiply \(r\) by each term in \(r^2 - 2r + 3\): \[ r \cdot r^2 = r^3 \] \[ r \cdot (-2r) = -2r^2 \] \[ r \cdot 3 = 3r \]

2. Multiply \(-1\) by each term in \(r^2 - 2r + 3\): \[ -1 \cdot r^2 = -r^2 \] \[ -1 \cdot (-2r) = 2r \] \[ -1 \cdot 3 = -3 \]

3. Combine all the results: \[ r^3 - 2r^2 + 3r - r^2 + 2r - 3 \]

4. Combine like terms:

   • The \(r^2\) terms: \(-2r^2 - r^2 = -3r^2\)
   • The \(r\) terms: \(3r + 2r = 5r\)

Putting it all together, the simplified polynomial is: \[ r^3 - 3r^2 + 5r - 3 \]

Now, to fill in the blanks in your question: \[ r^3 + (-3r^2) + 5r - 3 \]

Thus, the answer is: \[ r^3 - 3r^2 + 5r - 3 \]