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.

### Course: Get ready for AP® Calculus>Unit 1

Lesson 9: Factoring quadratics with perfect squares

# Factoring perfect squares

Sal factors 25x^2-30x+9 as (5x-3)^2 or as (-5x+3)^2. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• can't seem to solve this problem by grouping as Sal showed on the previous video. This is what I did:

25y squared - 30x + 9
25 * 9 = 225
Factors of 225:
1, 225
3, 75
5, 45
9, 25
15, 16
none of which whose sum is equal to 30.
In the last video, Sal stated that you first find the product of the first and last monomials, find the factors of that product whose sum is equal to the middle monomial, and from there you can group. I can't find factors of 225 whose sum equals -30. What am I doing wrong?
• actually 15 * 15 is 225 , not 15*16, so we have a.b = 225 and a+b = -30

so our factors are -15 and -15 thats why he said its a perfect square, so we have 25x^2-15x-15x+9 we factor 5x(5x-3)-3(5x-3) = (5x-3)(5x-3) = (5x-3)^2
• What software does Sal use?
• Sal uses a PC with:

Camtasia Recorder (\$200*)
SmoothDraw3 (Free)
Wacom Bamboo Tablet (\$80)

Prior to that, he used:

ScreenVideoRecorder (\$20)
Microsoft Paint (Free)

(1 vote)
• Do you have a video over regular factoring of trinomials? ex: 2x squared minus 3x minus 2. Ive been looking everywhere for a video of the sort.
• monomial, binomial, trinomial : the terminology goes down to?
• "mono" = one, as in one term
"bi" = two, as in two terms
"tri" = three, as in three terms.
This video is called "Factoring perfect square trinomials" because Sal is working with equations that have three terms.
• Why does it call trinomial?
(1 vote)
• tri means 3, so it has 3 terms. You might want to touch up on some older subjects if you don't what it means. Maybe some video about , binomials, and trinomials.
• When factoring your working on making it simpler correct?
• Factoring is the process of turning an expression into a multiplication problem.

Simplifying is the process of performing all possible operations.

So these processes actually have opposite results. To help clarify look at the following two example problems, one with the instructions factor, the other with the instructions simplify and look how each starts with the other's answer and ends with the other's question.

Example 1:
Simplify 3*5

Example 2:
Factor 15

Now for two Algebraic Examples

Example 3
Multiply (x+2)(x-3)
x^2-3x+2x-6

Example 4
Factor x^2-x-6
(x+?)(x-?)
(-3)(2)=6 and (-3)+(2)=-1
• why does ab have to be equal to -15? where did it come from?
• The pattern for a perfect square trinomial is:
a^2x^2 + 2abx + b^2

Sal is factoring 25x^2-30x+9
He uses the middle term from the pattern and from his trinomial to get: 2ab = -30
If you divide both sides by 2, you get ab = -15

Hope this helps.
• In the video, Sal showed us 2 possible answers to factor out the trinomial. So, if I have to answer this question like in a test or something, am I supposed to show the 2 possible answers even though they're the same or can I show one of the 2 possible answers for the question to mark right?
• It depends on what your teacher asks, or how the given prompt is worded. Factoring with the GCF is different, and factoring and polynomial is different.

(1 vote)
• Sorry if this question is off topic but what is the number e?
• Don't be sorry ;D
e is a mathematical constant. It is approximately 2.71828... (it goes on forever, it's irrational) and it is the base of the natural logarithm (no need to worry about any of that stuff until Algebra 2 or later lol xD). It is used in lots of financial matters and other things that I don't really know about xD.
A link to Wikipedia (which is always extensive and unnecessary but whatever xD):
http://en.wikipedia.org/wiki/E_%28mathematical_constant%29
Have a Happy New Year :)