Transcript Subtracting Polynomials
Ross is very much in love with his girlfriend, Raquel. For her birthday, he wants to give her something made with love. He found an old frame in his garage that he wants to fix up so he can frame a picture of himself to give to Raquel. In order to revamp the frame, he decides to order some scraps of fabric online.
The website offers various sizes of fabric. Ross needs to measure the frame before he decides how much fabric to buy. He needs to be careful because he doesn't want to include the space the picture will occupy in his measurements.
Polynomial Subtraction
To find the size of the frame, Ross can use polynomial subtraction. While browsing a doityourself blog, Ross finds two formulas to use. y₁ = 2x²  8x represents the area of the frame, including the picture. And y₂ = x²  2x  8 represents only the inner area of the frame. In order to find the area of the frame without the picture, Ross needs to subtract the area of the picture (y₂) from the area of the whole frame (y₁).
Vertical Method
There are two methods for doing this. First, let's do the vertical method. Make sure the polynomial expressions are in standard form. This means that the terms are in descending order according to their degree. Here they are.
When we subtract a polynomial, we need to make sure we subtract all of the terms. To do this, we need to distribute the minus, which is the same as multiplying by 1, to each term. Now we can add or subtract term by term according to the signs.
2x²  x² equals x². 8x +2x equals 6x, and because we don't have a constant in our first equation, we can add 0 plus 8, which equals 8. Ross just has to plug in the width of his frame for 'x' to find out how much fabric he needs.
Horizontal Method
Another way to subtract polynomials is by using the horizontal method. Again, first make sure that they are in standard form. We can distribute the subtraction sign to all terms inside the parentheses, just like we did before. So that gives us 2x²  8x  x² + 2x + 8. Now we can rearrange the order so that all of the like terms are next to each other, horizontally. 2x²  x² simplifies to x² then 8x + 2x combine to make 6x. 8 does not have any like terms to combine with, so we will just bring plus 8 down. The resulting answer is x² 6x +8.
Adding Vertically
Let's look at one more example. When adding vertically, put the expression in standard form, then make sure that all of the like terms are lined up together. Here we'll need to move the +2 so that it's above 4 because they're both constants. After combining like terms, you end up with 2x² +2x2.
But be careful! Sometimes you have polynomials that look like this. The first term has a combination of variables. It may seem like you can combine it with the other two terms but you canNOT. When combining terms, the variables need to look alike. They must have the same combination of variables and each variable must be raised to the same degree.
Alright, now that Ross has finished the frame he gets to give it to his girlfriend Raquel. But she isn't as excited as he thought she would be...because now she has 121 framed pictures of Ross...

Introduction to Polynomials – Naming Polynomials by Number of Terms

Adding Polynomials

Multiplying Polynomials

Multiplying Special Case Polynomials

Factoring out the GCF

Factoring Trinomials with a = 1

Factoring Trinomials with a ≠ 1

Factoring Special Case Polynomials

Factoring by Grouping

Subtracting Polynomials