If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:2:39

CCSS.Math: , ,

the quadratic expression x squared plus 5x plus C is a perfect square and it can be factored as X plus d squared both C and D are positive rational numbers so what I want to figure out in this video is what is C given the information that we have right over here what is C going to be equal to and what is d going to be equal to and like always pause the video and see if you can figure it out well let's work through this together we're saying that x squared plus 5x plus C can be re-written as X plus d squared so let me write that down so this part this part x squared plus 5x plus C we're saying that that could be written as X plus d squared this is equal to X plus d squared now we can rewrite X plus d squared is going to be equal to x squared plus 2x 2 let me write to DX 2 DX plus d squared if this step right over here you find strange I encourage you to watch the videos on squaring binomials or on our own perfect square polynomials either one so you can see the pattern that this is going to be x squared plus 2 times the product of both of these terms plus d squared and so when you look at it like this you can start you can start to pattern match a little bit you can say all right well 5 X right over here that is going to have to be equal to 2 D and then you can also say that C is going to have to be equal to d squared so once again we could say 2 D is equal to 5 2 D is equal to 5 or that D is equal to 5 halves so we figured out what D is equal to and now we can figure out what C is because we know that C is C needs to be equal to d squared C into that orange color actually so we know that C is equal to d squared which is the same thing as v hat squared we just figured out what D is equal to it's going to be 5 1/2 squared which is going to be 25 over 4 so C is C is equal to 25 over 4 D is equal to 5 halves and we're done