Question

Use the table to find each product. (3x^2+4x+8)(x^2 + 3x)

3x^2 | 4x | 8
x^2| answer | answer | answer |
3x | answer | answer | answer |

Combine like terms and find the final product
Product: ________

Answer 1

To find the product of the polynomials \( (3x^2 + 4x + 8)(x^2 + 3x) \) using the table method, we multiply each term in the first polynomial by each term in the second polynomial and then combine like terms.

We will fill in the table with the products:

| | \(3x^2\) | \(4x\) | \(8\) |
|----------|-------------|-------------|-------------|
| \(x^2\) | \(3x^4\) | \(4x^3\) | \(8x^2\) |
| \(3x\) | \(9x^3\) | \(12x^2\) | \(24x\) |

Now let's summarize the products from the table:

1. \(3x^2 \cdot x^2 = 3x^4\)
2. \(3x^2 \cdot 3x = 9x^3\)
3. \(4x \cdot x^2 = 4x^3\)
4. \(4x \cdot 3x = 12x^2\)
5. \(8 \cdot x^2 = 8x^2\)
6. \(8 \cdot 3x = 24x\)

Now we can combined the like terms together:

- \(3x^4\)
- \(9x^3 + 4x^3 = 13x^3\)
- \(12x^2 + 8x^2 = 20x^2\)
- \(24x\)

Putting it all together:

\[
3x^4 + 13x^3 + 20x^2 + 24x
\]

Thus, the final product is:

**Product: \(3x^4 + 13x^3 + 20x^2 + 24x\)**