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Chapter 0: Problem 98

Explain how to subtract polynomials.

Short Answer

Expert verified
To subtract polynomials, first arrange the polynomials by matching like terms. Then perform subtraction term by term from the highest degree to the lowest. The result is a new polynomial that is the difference of the given polynomials.

Step by step solution

01

Understand the Polynomial Structures

Polynomials are algebraic expressions comprising of terms, which are variables raised to different powers and multiplied by coefficients. Each term in a polynomial is separated by a '+' or '-' sign. For instance, \(3x^2 - 2x + 1\) is a polynomial and \(3x^2\), \(-2x\), \(1\) are its terms.
02

Arrange Polynomials by Matching Terms

Before subtracting, arrange the polynomials in descending order of their power and line up matching terms vertically. If a term is missing in one polynomial, you may insert a term with a zero coefficient to fill the gap. For example, if we were to subtract \(2x^2 - 3x + 2\) from \(3x^2 - x\), the polynomials are firstly arranged as \(3x^2 - x + 0\) and \(2x^2 - 3x + 2\).
03

Perform the Subtraction

Then perform the subtraction for each aligned pair of terms starting from the highest degree. In our example, \(3x^2 - 2x^2 = x^2\), \(-x - (-3x) = 2x\), and \(0 - 2 = -2\). Thus, \(3x^2 - x - (2x^2 - 3x + 2) = x^2 + 2x - 2\).

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