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: ________
Options:
3x^4
9x^3
12x^3
8x^2
24x
4x^3
3x^2 | 4x | 8
x^2| answer | answer | answer |
3x | answer | answer | answer |
Combine like terms and find the final product
Product: ________
Options:
3x^4
9x^3
12x^3
8x^2
24x
4x^3
Answers
GPT-4o mini
To find the product of \((3x^2 + 4x + 8)(x^2 + 3x)\), we can use the distributive property (often referred to as the "box" method).
We fill in the table as follows:
\[
\begin{array}{c|ccc}
& 3x^2 & 4x & 8 \\
\hline
x^2 & 3x^4 & 4x^3 & 8x^2 \\
3x & 9x^3 & 12x^2 & 24x \\
\end{array}
\]
Now we calculate each entry of the table:
1. **For \(3x^2\):**
- \(3x^2 \cdot x^2 = 3x^4\)
- \(3x^2 \cdot 3x = 9x^3\)
2. **For \(4x\):**
- \(4x \cdot x^2 = 4x^3\)
- \(4x \cdot 3x = 12x^2\)
3. **For \(8\):**
- \(8 \cdot x^2 = 8x^2\)
- \(8 \cdot 3x = 24x\)
Now, let's fill in the table:
\[
\begin{array}{c|ccc}
& 3x^2 & 4x & 8 \\
\hline
x^2 & 3x^4 & 4x^3 & 8x^2 \\
3x & 9x^3 & 12x^2 & 24x \\
\end{array}
\]
Next, we combine the like terms from the entries we calculated:
- \(3x^4\)
- \(4x^3 + 9x^3 = 13x^3\)
- \(8x^2 + 12x^2 = 20x^2\)
- \(24x\)
So, the final product is:
\[
3x^4 + 13x^3 + 20x^2 + 24x
\]
Since the options provided do not include all terms, the answer appears to lean towards you needing information about just the \(x^3\) term.
### Product:
The coefficient of \(x^3\) in the final product is \(13\).
None of the individual terms from the options (that represent coefficients of \(x^3\)) match this, so you'd typically put "13x^3” or simply refer to each part only if indicated.
Let me know if you need clarification or further assistance!
We fill in the table as follows:
\[
\begin{array}{c|ccc}
& 3x^2 & 4x & 8 \\
\hline
x^2 & 3x^4 & 4x^3 & 8x^2 \\
3x & 9x^3 & 12x^2 & 24x \\
\end{array}
\]
Now we calculate each entry of the table:
1. **For \(3x^2\):**
- \(3x^2 \cdot x^2 = 3x^4\)
- \(3x^2 \cdot 3x = 9x^3\)
2. **For \(4x\):**
- \(4x \cdot x^2 = 4x^3\)
- \(4x \cdot 3x = 12x^2\)
3. **For \(8\):**
- \(8 \cdot x^2 = 8x^2\)
- \(8 \cdot 3x = 24x\)
Now, let's fill in the table:
\[
\begin{array}{c|ccc}
& 3x^2 & 4x & 8 \\
\hline
x^2 & 3x^4 & 4x^3 & 8x^2 \\
3x & 9x^3 & 12x^2 & 24x \\
\end{array}
\]
Next, we combine the like terms from the entries we calculated:
- \(3x^4\)
- \(4x^3 + 9x^3 = 13x^3\)
- \(8x^2 + 12x^2 = 20x^2\)
- \(24x\)
So, the final product is:
\[
3x^4 + 13x^3 + 20x^2 + 24x
\]
Since the options provided do not include all terms, the answer appears to lean towards you needing information about just the \(x^3\) term.
### Product:
The coefficient of \(x^3\) in the final product is \(13\).
None of the individual terms from the options (that represent coefficients of \(x^3\)) match this, so you'd typically put "13x^3” or simply refer to each part only if indicated.
Let me know if you need clarification or further assistance!