(6x^2-x-8)(x^2+x+2)

Jasonbradley

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Jun 16, 2024

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Multiplying Polynomials: (6x² - x - 8)(x² + x + 2)

This article will guide you through multiplying the two polynomials (6x² - x - 8) and (x² + x + 2).

Understanding the Process

Multiplying polynomials involves distributing each term of one polynomial to every term of the other. This is similar to the distributive property of multiplication you learned in basic algebra.

The Steps

1. Distribute the first term of the first polynomial:

   • Multiply 6x² by each term of the second polynomial:
     • 6x² * x² = 6x⁴
     • 6x² * x = 6x³
     • 6x² * 2 = 12x²

2. Distribute the second term of the first polynomial:

   • Multiply -x by each term of the second polynomial:
     • -x * x² = -x³
     • -x * x = -x²
     • -x * 2 = -2x

3. Distribute the third term of the first polynomial:

   • Multiply -8 by each term of the second polynomial:
     • -8 * x² = -8x²
     • -8 * x = -8x
     • -8 * 2 = -16

4. Combine like terms:

   • 6x⁴ + 6x³ - x³ + 12x² - x² - 8x² - 2x - 8x - 16
   • 6x⁴ + 5x³ + 3x² - 10x - 16

The Result

Therefore, the product of (6x² - x - 8) and (x² + x + 2) is 6x⁴ + 5x³ + 3x² - 10x - 16.

Key Takeaways

• Remember to distribute each term of the first polynomial to every term of the second polynomial.
• Combine like terms carefully to simplify the final expression.
• This process can be applied to multiply any pair of polynomials.