Here’s a problem where I’m given a trinomial and the leading coefficient number is 1. I’m asked to factor. The1 shows up right here. So here’s what I’m going to be thinking about. I’m going to be looking for 2 numbers who add up to 12 and who multiply to 20. Some of you guys can do this in your head in like 10 seconds. Sometimes problems are more difficult than this. So I’m going to show you a strategy of how you could approach this if you couldn’t do it in your head like that.
First thing I would do is think about factors of 20, pairs that multiply to 20. It could be 1 and 20, it could be 2 and 10, and it could be 4 and 5. I think that’s it. These are all the pairs that multiply to 20. I’m looking for one of these pairs whose sum is 12. Here it is right here. That’s how I know my answer is going to look like this, x plus 2 and x plus 10. That’s the factor form or the product form of this trinomial. I could check my work by foiling. I’ll do it really quickly so you guys can see.
Foiling means firsts, outers, inners, lasts and when I combine my terms I do in deed get x squared plus 12x plus 20. That’s how I can check my work and know I did it correctly. And the way I did it was by finding 2 numbers whose sum was this and whose product was that. That’s always the process you use for factoring trinomials when your leading coefficient is 1.
One other thing I want to show you before I let you move on to your homework problems is to make sure your trinomial is in standard form first. Standard form meaning your x term shows up in the middle of the trinomial and your constant term is at the end. It’s the x term or x to the first term whose coefficient is the sum and the constant term, represents the product. If you can keep that straight in your head these will be really quick problems for you.
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