Problem 98 - College Algebra Essentials

Question

Explain how to subtract polynomials.

Step-by-Step Solution

Answer

Subtracting polynomials involves arranging the polynomials vertically by like terms, changing the sign of each term of the second polynomial, and then adding vertically. After performing the addition/subtraction, simplify the polynomial if possible by combining like terms.

Step 1: Arrange the Polynomials

Write down the polynomials to be subtracted from each other in a column format. This allows for easy matching of like terms. Like terms are those which have exactly the same variables and powers. For example, \(2x^2\) and \(3x^2\) are like terms, while \(2x^2\) and \(3x\) are not.

Step 2: Apply the Subtraction

Subtract each term of the second polynomial from the corresponding term of the first polynomial. Remember that subtracting a number is the same as adding its negative. Therefore, change the sign of each term of the second polynomial and then add the terms vertically.

Step 3: Simplify the Polynomial

After performing the addition/subtraction, simplify the polynomial if possible. Combine any like terms that may have resulted from the subtraction.