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

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

Polynomial Subtraction: A Step-by-Step Guide

This article will guide you through the process of subtracting the polynomial (1/4)x³ - (5/2)x² + (3/5)x + (1/4) from (6/5)x² - (4/5)x³ + (5/6) + (3/2)x.

Understanding the Process

Subtracting polynomials involves combining like terms with careful attention to signs. We will distribute the negative sign to each term of the polynomial being subtracted and then combine the coefficients of similar terms.

Step-by-Step Solution

  1. Rewrite the problem:

    • (6/5)x² - (4/5)x³ + (5/6) + (3/2)x - [(1/4)x³ - (5/2)x² + (3/5)x + (1/4)]

  2. Distribute the negative sign:

    • (6/5)x² - (4/5)x³ + (5/6) + (3/2)x - (1/4)x³ + (5/2)x² - (3/5)x - (1/4)

  3. Combine like terms:

    • (-4/5)x³ - (1/4)x³ + (6/5)x² + (5/2)x² + (3/2)x - (3/5)x + (5/6) - (1/4)

  4. Simplify by finding common denominators and combining:

    • (-16/20)x³ - (5/20)x³ + (24/20)x² + (50/20)x² + (15/10)x - (6/10)x + (20/24) - (6/24)
    • (-21/20)x³ + (74/20)x² + (9/10)x + (14/24)

  5. Simplify further:

    • -(21/20)x³ + (37/10)x² + (9/10)x + (7/12)

The Result

Therefore, the result of subtracting (1/4)x³ - (5/2)x² + (3/5)x + (1/4) from (6/5)x² - (4/5)x³ + (5/6) + (3/2)x is -(21/20)x³ + (37/10)x² + (9/10)x + (7/12).

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