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

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
 Multiply 6x² by each term of the second polynomial:

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
 Multiply x by each term of the second polynomial:

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
 Multiply 8 by each term of the second polynomial:

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.