(6x^3-5x^2+4x-1) (2x^2-x+1)

2 min read Jun 16, 2024
(6x^3-5x^2+4x-1) (2x^2-x+1)

Multiplying Polynomials: (6x^3 - 5x^2 + 4x - 1)(2x^2 - x + 1)

This article will guide you through the process of multiplying two polynomials: (6x^3 - 5x^2 + 4x - 1) and (2x^2 - x + 1).

Understanding the Process

Multiplying polynomials involves distributing each term of the first polynomial to every term of the second polynomial. We can visualize this as a table:

2x² -x 1
6x³ 12x⁵ -6x⁴ 6x³
-5x² -10x⁴ 5x³ -5x²
4x 8x³ -4x² 4x
-1 -2x² x -1

Steps for Multiplication

  1. Distribute: Multiply each term of the first polynomial by each term of the second polynomial.

  2. Combine Like Terms: After distribution, combine terms with the same variable and exponent.

Calculating the Result

Following the steps above, we get:

  • 12x⁵ + (-6x⁴ - 10x⁴) + (6x³ + 5x³ + 8x³) + (-5x² - 4x² - 2x²) + (4x + x) - 1

Simplifying:

12x⁵ - 16x⁴ + 19x³ - 11x² + 5x - 1

Conclusion

The product of (6x^3 - 5x^2 + 4x - 1) and (2x^2 - x + 1) is 12x⁵ - 16x⁴ + 19x³ - 11x² + 5x - 1. This process demonstrates the distributive property of multiplication and its application to polynomial expressions.

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