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Adding and Subtracting Polynomials - Problem 1

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

In this problem, I’m given two trinomials and asked to add them together. So in order to do this you might want to rewrite them and add vertically. I personally think that’s a little too much writing. I just like to look for terms that have the same degree and combine them. Like for example, first thing I’m going to look for is everything that has a p to the third power. There is this guy, 2p to the third power and then I have plus 3 more p to the thirds altogether that’s going to give me 5p to the third which is also sometimes called p cubed. That’s the same meaning, just different words p to the third or p cubed.

Okay, now I’m going to look for my p². I have 6p²take away 8 p², careful with that minus. 6 take away 8 gives me -2p² and then last but not least I’m going to look for my p to the first, in its regular p terms. Here is 9 of them plus -11. 9 plus -11 is -2, so I’m left with -2p at the end there. That’s my final answer.

If you choose to use this method, it’s totally fine, just be really careful that every term in both polynomials was accounted for. It got written in your final answer somehow and also please be careful with minus signs like this negative 8p² which is really important.

A common mistake students would make will to do okay 6p squared plus 8 p squared I bet you a lot of kids would have 14p squared right there. Just be really careful with the minus signs, and this problem should not be too tricky for you on your homework.

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