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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.

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• At , can someone explain how d is turned into 5/2? Also explain how 2d equals 5, and not 2dx.
• 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.
• So perfect square pattern is just a shortcut method like cross multiply?

And the general form if using grouping method?
• 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.
• This problem is so confusing. I can't comprehend how 5/2 would give us the answer. Arenโt the factors of d^2 suppose to equal 5x when added together?
• Can the answer be represented as a decimal?
• You could, but sometimes, it's just easier to answer in fractional form. :)
(1 vote)
• 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.
• At sal says that the numbers are posotive rational numbers. What does this mean?
• 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.
(1 vote)
• I'm kind of confused like what will I do for a question like 9x^2 + 6x +1?
(1 vote)
• Is 9x^2 a perfect square? Yes. It is (3x)^2
Is 1 a perfect square? Yes. It is 1^2
Does 2(3x)(1) = 6x? Yes.
So, this is a perfect square trinomial.
The factors are: (3x+1)(3x+1) or (3x+1)^2

Hope this helps.