Asked by Yes.

Multiply the polynomials (5x−2)(6x+3)

(1 point)
30x^2+3x+
Finish the Equation.
Answered by Yes.
The negative sign in the equation has to be positive in order to be correct.
Answered by Yes.
The Negative constant term (-6) Should in fact be a positive number
Answered by GPT-4o mini
To multiply the polynomials \( (5x - 2)(6x + 3) \), we can use the distributive property (also known as the FOIL method for binomials).

1. First, we distribute \( 5x \) to both terms in the second polynomial:
\[
5x \cdot 6x = 30x^2
\]
\[
5x \cdot 3 = 15x
\]

2. Next, we distribute \( -2 \) to both terms in the second polynomial:
\[
-2 \cdot 6x = -12x
\]
\[
-2 \cdot 3 = -6
\]

3. Now, we combine all these results:
\[
30x^2 + 15x - 12x - 6
\]

4. Combine the like terms (\( 15x - 12x \)):
\[
30x^2 + 3x - 6
\]

Therefore, the final result of multiplying the polynomials \( (5x - 2)(6x + 3) \) is:
\[
30x^2 + 3x - 6
\]

So, you can finish the equation as:
\[
30x^2 + 3x - 6
\]
Answered by GPT-4o mini
Let me clarify the multiplication of the polynomials \((5x - 2)(6x + 3)\) once more to ensure we have the correct signs.

1. Using the distributive property (or FOIL method):

- First:
\[
5x \cdot 6x = 30x^2
\]

- Outside:
\[
5x \cdot 3 = 15x
\]

- Inside:
\[
-2 \cdot 6x = -12x
\]

- Last:
\[
-2 \cdot 3 = -6
\]

2. Now we combine all these terms:
\[
30x^2 + 15x - 12x - 6
\]

3. Now, combine the like terms (\(15x - 12x\)):
\[
30x^2 + (15x - 12x) - 6 = 30x^2 + 3x - 6
\]

So the final product is indeed:

\[
30x^2 + 3x - 6
\]

If you're indicating that a term should be positive, could you please specify which term you're referring to? As per the calculations, the product does indeed yield a negative constant term \(-6\). If there is confusion, please clarify so I can provide the accurate assistance needed!
Answered by GPT-4o mini
Let’s carefully re-evaluate the multiplication of the polynomials \((5x - 2)(6x + 3)\) step-by-step to confirm the final result:

1. **Using the distributive property (FOIL method):**

- **First:**
\[
5x \cdot 6x = 30x^2
\]

- **Outside:**
\[
5x \cdot 3 = 15x
\]

- **Inside:**
\[
-2 \cdot 6x = -12x
\]

- **Last:**
\[
-2 \cdot 3 = -6
\]

2. **Combine all the terms:**
\[
30x^2 + 15x - 12x - 6
\]

3. **Combine the like terms (\(15x - 12x\)):**
\[
30x^2 + (15x - 12x) - 6 = 30x^2 + 3x - 6
\]

The expression we have derived is:
\[
30x^2 + 3x - 6
\]

But since you mentioned that the constant term should be positive, let’s reevaluate the situation:

The initial expression given is \((5x - 2)(6x + 3)\). Verify to see if there might have been a sign or term that was misinterpreted. If we consider:

1. The negative from \(-2\) remains when multiplied by \(3\), leading indeed to \(-6\).
2. The \(5x\) multiplied by \(3\) (the positive) results correctly as \(15x\).

Thus, the negative constant term \(-6\) arises directly from the multiplication \( (-2) \cdot 3 \).

### Conclusion

Based on this multiplication, the polynomial product is:

\[
30x^2 + 3x - 6
\]

I assure you that the signs derived from the steps above are correct based on standard polynomial multiplication. If the expected result was different, please double-check the original polynomials or any additional context that may affect the interpretation. I’m here to help!