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Chapter 0: Problem 98

Explain how to subtract polynomials.

Short Answer

Expert verified
To subtract polynomials, distribute any negative sign present before a polynomial, line up like terms of the polynomials, perform subtraction term by term, and combine any remaining like terms.

Step by step solution

01

Distribute any Negative Sign

If a negative sign is right before a polynomial, distribute it to all the terms inside the polynomial. This changes the sign of all the terms inside the brackets. For instance, \( -(2x^2 + 5x - 3) \) changes to \( -2x^2 - 5x + 3 \). Doing this helps when subtracting the polynomials later.
02

Line up Like Terms

Align like terms under one another. Like terms are terms with the same variable(s) and exponent(s). For instance, if you're subtracting \( 4x^3 - 2x^2 + 8x - 1 \) from \( 3x^3 + x^2 - 5x +2 \), arrange them like so: \[ \begin{align*} & 4x^3 - 2x^2 + 8x - 1 \ - & 3x^3 + x^2 - 5x + 2 \end{align*} \] This makes it easier to subtract.
03

Perform Subtraction

Subtract the lower polynomial from the upper polynomial term by term. Subtract coefficients of like terms from each other. Continuing from the previous example, \( (4x^3 - 3x^3) - (2x^2 - x^2) + (8x - -5x) - (1 - 2) \) results in: \( x^3 - x^2 - 13x - 3 \)
04

Combine Like Terms

Upon subtracting, if there are like terms, combine them by addition or substraction. In our example, there are no like terms left to combine, so our final polynomial is: \( x^3 - x^2 - 13x - 3 \)

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Most popular questions from this chapter

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