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### Course: Algebra 1 > Unit 13

Lesson 8: Factoring quadratics with perfect squares- Perfect square factorization intro
- Factoring quadratics: Perfect squares
- Perfect squares intro
- Factoring perfect squares
- Identifying perfect square form
- Factoring perfect squares: negative common factor
- Factoring perfect squares: missing values
- Factoring perfect squares: shared factors
- Perfect squares

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# 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.(33 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.(8 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)
- 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!(3 votes)
- Yes, or else if a trinomial cannot form (a ± b)², then it isn't a perfect square.(2 votes)

- 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.(6 votes)

- 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.(3 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.(5 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!(3 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)

- Just want to ask a quick question, what is the point of earning energy point?? Does it give me energy?? Just curious.:) ^-^(2 votes)
- You can unlock avatars and badges with it.(2 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.