Polynomial factors and graphs — Basic example

- [Instructor] Given the polynomial above, what are its zeros? So the zeros of this polynomial are going to be the x values that make it equal to 0. So it's going to be the x values that make this expression equal to 0, or you could say the x values that satisfy this equation. Because if you satisfy this equation, you're making this expression equal to 0. So what are those x values going to be? Well, if I take the product of two things, and if they're going to be equal to 0, I can get 0 by if one or both of these are equal to 0, because 0 times anything is 0. So x + 7 could be equal to 0. Or another way to solve this is for x - 10 to be equal to 0. So the zeros here, well, how do we get x + 7 to be equal to 0? Well, subtract 7 from both sides. X could be -7. And if I add 10 to both sides here, x could be equal to 10. Either of these is going to make this expression equal to 0. You could see that. If x is equal to -7, this is going to be 0. 0 times anything here, the whole thing's gonna be 0. If x is going to be equal to 10, this expression's gonna be 0, and then the whole thing's gonna be 0. So x is equal to -7 and x is equal to 10, which is that choice (laughs). Wasn't able to circle it in on-- that choice right over there, x = -7 and x is equal to 10.