Polynomial Subtraction: A StepbyStep 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.
StepbyStep Solution

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)]

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)

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)

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)

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).