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

Course: Get ready for Algebra 2>Unit 1

Lesson 9: Factoring quadratics with perfect squares

Factoring perfect squares: missing values

Sal analyzes the factorization of x^2+5x+c as (x+d)^2 to find the values of the missing coefficients c and d.

Want to join the conversation?

• At , can someone explain how d is turned into 5/2? Also explain how 2d equals 5, and not 2dx.
(14 votes)
• Hopefully, you can see that the 2 middle terms must equal. You can use: "2dx = 5x" or you can just use Sal's version: "2d = 5". If you solve either of these for "d", you will get "d = 5/2".
-- if you start with: "2dx = 5x", you need to divide by "2x" to solve for "d"
2dx / (2x) = 5x / (2x)
d = 5x / (2x) Reduce
d = 5/2
-- if you start with "2d = 5", just divide both sides by 2 and you get d = 5/2

Hope this helps.
(31 votes)
• This problem is so confusing. I can't comprehend how 5/2 would give us the answer. Aren’t the factors of d^2 suppose to equal 5x when added together?
(6 votes)
• So perfect square pattern is just a shortcut method like cross multiply?

And the general form if using grouping method?
(3 votes)
• Yes... if you have a perfect square trinomial, you can use the pattern as a quicker way to do the factoring. The pattern can also be used to square 2 binomials because it creates the perfect square trinomial.
(7 votes)
• I'm so confused bc how did he get 5/2 and that turned into 25/4?
(2 votes)
• Why couldn't we just assume that c is the square of the middle coefficient and therefore 25, and then factor it out into (x+5)(x+5), so then d=5?
(1 vote)
• That would give you x^2+10x+25 since you end up with two 5x terms, so you have changed the problem.
(4 votes)
• Is this method used to solve linear equations?
(1 vote)
• No, linear equations are 1st degree (highest exponent = 1). Factoring is used for 2nd degree and higher equations.
(4 votes)
• Can the answer be represented as a decimal?
(2 votes)
• You could, but sometimes, it's just easier to answer in fractional form. :)
(0 votes)
• It's not a perfect square if it's a decimal or fraction though?
(2 votes)
• Yes, decimals and fractions can be squares. For example, 0.25 is the square of 0.5, as 0.5x0.5=0.25.

Hope that helped!
(2 votes)
• Please, correct me if I'm wrong, but from what I understand: (a +/- b)^2 can only be used for "perfect square" trinomials and for every other trinomial, with highes degree ^2, we use the "a x b = A x C and a+b=B" technique. I will greatly appreciate if anyone, confident in their answer, clarifies this for me. Thank you!
(2 votes)
• Yes, or else if a trinomial cannot form (a ± b)², then it isn't a perfect square.
(2 votes)
• Where did you get 5/2?
(1 vote)
• When you square a binomial, you get a very specific pattern. Sal shows this using (x+d)^2 = x^2+2dx+d^2
Notice, the middle term has a coefficient of 2d, and the last term is d^2.

Sal was given x^2+5x+c and asked to find c. Using the pattern, he know that 5 = 2d. Solve it and you get d=5/2. Then again using the pattern, he knows c = d^2. So c = (5/2)^2 = 25/4.

Hope this helps.
(4 votes)

Video transcript

- [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.