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: Algebra (all content)>Unit 10

Lesson 16: Factoring polynomials with quadratic forms

# Factoring quadratics: negative common factor + grouping

Sal factors -12f^2-38f+22 as -2(2f-1)(3f+11). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• This isn't in the video, but I don't know where else to ask it:
While doing the exercise, I got -7x²-10x-3, and I simplified it like

-7x² - 10x - 3
-7x² (-7x - 3x) - 3
(-7x² -7x) (-3x-3)
-7x(x) -3(x)
x(-7x-3)

According to the test, this was wrong. Can someone explain why?
• When you factored, you dropped you constant term. Here is the correct way to do it:
-7x² - 10x - 3
− (7x² + 10x + 3)
− (7x² + 7x + 3x + 3)
− [(7x(x + 1) + 3(x + 1)]
− (x+1)(7x + 3)
• i got -2(-3x-11)(2x-1) is that correct?
• Close, you made two small errors.
The variable was an f and you changed it to a x. No big deal, but you the letter in the answer shoudl still be f.
and second, your (-3x-11) shoudl be (+3f-11) the sign on the 3 should be positive.
Check you work and see where you missed the sign.
Good luck
• This might be a weird question but how would you solve for what f is??
• is there any other way to solve the problem besides writing it out?
• i have a question that is (x+2)^2 - (x+2) - 42 does this go to 4x^2 - 2x - 42? and if so what do i do then?
• You can substitute a plain x for (x+2) and factor first to make it easier, but then you have to replace it back. So it becomes x^2-x-42. Then facor that: (x-7)(x+6)then plug the (x+2) back in for the x.

If you multiply (x+2)^2 first it equals x^2+4x+4 not 4x^2 so be careful and remember to foil. This method is more work, but it would be x^2+4x+4-x-2-42
after simplifying it would be x^2+3x-40. Then factor to (x+8)(x-5) ANSWER
• At , Mr.Khan says to try a few numbers that add to 19 and multiply to -66. This works for small numbers, but what about if you have a really LARGE quadratic to factor? Then it would take a very long time to find the 2 numbers. I have been searching up methods, and the quickest one I found was the prime factorization method. However, this is still taking too long. My quadratic I am trying to factor is 84x^2+181x-90. Multiplying the 84 and -90 gets me to 7260, but it is taking me too long to figure out what 2 numbers multiply to that and add to 181. I am looking for a method I can use to factor these really fast because in my math counts competition I cant spend forever on one question.

Thanks!
• Why does a times b have to be -66 and a + b have to be 19?
• Is there any way to do this a little faster? It takes a lot of time to do, and I have a time limit on all of my tests and quizzes.
• Just practice a lot! Once you really understand it, (you still have to do each step) you can do the steps faster. From experience, I can say that after doing these for about a week or so, I've really gotten the hang of it, from doing about 20+ factoring polynomials a day! Hope this helps!
• I got -2(-3f-11)(-2f+1). Does anyone care to share why this differs from Sal's presumably optimal answer?
• You have extra factors of -1 applied to both your binomials. This is why your signs are different. If you factor out those -1's, you can get to Sal's version
-3f-11 = -1(3f+11)
-2f+1 = -1(2f-1)

You now have: -2(-1)(-1)(3f+11)(2f-1)
Multiply the 3 constants to get Sal's final version of: -2(3f+11)(2f-1)

To get your version, you would have had to make a conscious decision to factor out -3f when Sal factored out +3f, and then you did the same late by factor out a -2f when Sal did +2f. That's what caused the extra factors of -1 to creep in.

To avoid this situation in the future, only factor out a negative value if you need to change the highest degree term to be positive. They were already positive in this problem after the GCF of -2 had been factored out.

Hope this helps.