Main content

## Algebra 1 (Eureka Math/EngageNY)

### Course: Algebra 1 (Eureka Math/EngageNY) > Unit 4

Lesson 4: Topic A: Lessons 3-4: Special forms- Factoring difference of squares: leading coefficient ≠ 1
- Factoring difference of squares: analyzing factorization
- Factoring difference of squares: missing values
- Factoring difference of squares: shared factors
- Difference of squares
- Factoring perfect squares
- Identifying perfect square form
- Factoring higher-degree polynomials: Common factor
- Factoring perfect squares: negative common factor
- Factoring perfect squares: missing values
- Factoring perfect squares: shared factors
- Perfect squares

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# 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?

- At2:00, 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.(28 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?(7 votes)
- So perfect square pattern is just a shortcut method like cross multiply?

And the general form if using grouping method?(4 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.(6 votes)

- At0:13sal says that the numbers are posotive rational numbers. What does this mean?(3 votes)
- Positive means it is not a negative number and rational means is a number that does not have a decimal that goes on forever. Sal is basically saying this question is playing by the rules as we know at this point and there is no weird stuff going on.(2 votes)

- In this video how did he get d=5/2 someone please explain to me thank you.(2 votes)
- since (x+b)^2 = x^2 + 2bx + b^2, note that the middle term is 2b. So if 2b = 5, then b = 5/2 and b^2 = 25/4. So to complete the square, you have to divide the coefficient of the x term by 2.(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. :)(1 vote)

- Sal explains we can "pattern match" to figure out why 2d = 5 https://youtu.be/oIslHyWJHEY?t=91(1 vote)

- I'm so confused bc how did he get 5/2 and that turned into 25/4?(2 votes)
- Get in the habit of looking at the top rated questions and answers. David Severin provided a very good response to this question. You can find it at: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/solving-for-constants-in-perfect-square-polynomial?qa_expand_key=ag5zfmtoYW4tYWNhZGVteXI_CxIIVXNlckRhdGEiHGthaWRfNTQ1MjU0MTY5ODgxMDMwNDQxMTMwNDYMCxIIRmVlZGJhY2sYgIDV77DJzQgM&qa_expand_type=answer

Note: Copy & paste the entire text string into your browser to get to the specific answer.(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)

## 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.