How to Subtract Polynomial Equations

As if algebra could not get anymore complicated, you then come faced to face with having to figure out how to subtract polynomial equations. A typical polynomial will be an expression that is constructed from variables (x), exponents and constants (a whole number). It may look something like this: (-3x^2 + 5x – 1). Then someone decided that we could actually subtract one polynomial from another, adding a little twist into the games we can play with numbers. It is highly likely that you will come across a problem that will ask you to simplify two polynomials by subtracting them, and it may look something like this: (-3x^2 + 5x – 1) – (-5 x^2 + 8x – 3). You may begin to feel a bit panicky at the thought of attempting to work out a problem like this, but attacking a polynomial like this is fairly simple.

Instructions

Difficulty: Moderately Easy

1. Write the problem down on a piece of scrap paper before you write it in your notebook. This way you can make all mistakes on the scrap paper, and copy the completely worked out problem into your book, neatly.
2. Work the problem out horizontally, by writing the first polynomial beneath the problem.
3. Place an imaginary 1 in front of the parentheses of the first polynomial. It will look like this: 1(-3x^2 + 5x – 1).
4. Use the distributive property to remove the parentheses. The distributive property will have you multiplying the imaginary 1 against the whole numbers in the first polynomial.
5. Write down the second polynomial and place an imaginary 1 in front of the parentheses. In this case, however, there is also the subtraction sign which will work as a negative sign and will make your imaginary 1 a -1. It should look like this: -1(-5 x^2 + 8x – 3).
6. Use the distributive property to remove the parentheses from the second polynomial. To do this, you will multiply the -1 against the whole numbers in the first polynomial. Remember to look for positive and negative signs and follow the proper rule for multiplying positive and negative numbers.
7. Rewrite the results of the new equation, which should look like this:
   -3x^2 + 5x – 1 +5 x^2 – 8x + 3.
8. Combine like terms to simplify the equation.

Tips & Warnings

• Learn and study the rules associated with adding and subtracting integers.