Ask a New Question
Menu

Multiply the polynomials (5x−2)(6x+3)

(1 point)
30x^2+3x+
Finish the Equation.

5 answers

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

The negative sign in the equation has to be positive in order to be correct.

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!

The Negative constant term (-6) Should in fact be a positive number

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!