Whatever's my constant term, myĪ times b, the product has to be that. You should put it in that form, so that you canĪlways say, OK, whatever's on the first degree coefficient, And of course, this has toīe in standard form. You take their product, have to be equal to 9. Say, all right, what two numbers add up to thisĬoefficient right here? And those same two numbers, when Leading coefficient on this quadratic is a 1, you can just This, when the coefficient on the x squared term, or the Videos, you'll see that it is indeed x squared plusġ0x, plus 9. Out, using the skills we developed in the last few So we could factor thisĪs being x plus 1, times x plus 9.

So a could be equal to 1, andī could be equal to 9. You'll have 3 plus 3- that doesn't equal 10. So what are the factors of 9? They're 1, 3, and 9. And normally when we'reįactoring, especially when we're beginning to factor, What are the factors of 9? What are the things that aĪnd b could be equal to? And we're assuming thatĮverything is an integer.

Match this to that? Is there some a and b whereĪ plus b is equal to 10? And a times b is equal to 9? Well, let's just think about Middle coefficient on the x term, or you could say theįirst degree coefficient there, that's going to be This is the product of two binomials, we see that this Plus- I can write it as b plus a, or a plusī, x, plus ab. In the middle right here, because they're bothĬoefficients of x. X squared, plus x times b, which is bx, plus a times x,

Two things, what happens? Well, we have a little bit What happens if we were to take x plus a, and multiply How do we do that? Well, let's just think about Quadratic expression, x squared plus 10x, plus 9. In this case, in all of theĮxamples we'll do, it'll be x. Have a variable raised to the second power. Polynomial, or just a quadratic itself, or quadraticĮxpression, but all it means is a second degree polynomial. Bunch of examples of factoring a second degree polynomial,

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