Factoring quadratics with perfect squares
- [Voiceover] The quadratic expression x-squared plus five x plus c is a perfect square. It can be factored as x plus d-squared. Both c and d are positive rational numbers. What I wanna 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? Like always, pause the video and see if you can figure it out. Let's work through this together. We're saying that x-squared plus five x plus c can be rewritten as x plus d-squared. Let me write that down. So this part, this part, x-squared plus five x 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 two 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 perfect square polynomials, either one, so you can see the pattern that this is going to be. X squared plus two times the product of both of these terms plus d-squared. When you look at it like this, you can start to pattern match a little bit. You can say, alright, five x, right over here, that is going to have to be equal to two d, and then, you can also say, that c is going to have to be equal to d-squared. Once again, you can say two d is equal to five, two d is equal to five, or that d is equal to five halves. We've figured out what d is equal to. Now we can figure out what c is, because we know that c needs to be equal to d-squared, gimme that orange color, actually, so we know that c is equal to d-squared, which is the same thing as five halves, squared. We just figured out what d is equal to. Gonna be five halves, squared, which is going to be 25 over four. C is equal to 25 over four, d is equal to five halves. We're done.