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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.

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• I'm confused because the way I did gave me (3x + 11)(-4x + 2). I'm going to lose points in my exams doing it in my way ? I'm worried about that.
• The way U did it its OK.

Coz the main reason for factoring is to find out the values of the variable 'x'.

In this case u have 2 values

x=-11/3 and x=2/4 or 1/2.

let me break it down though...

-12x2-38x+22

=-12x2+6x-44x+22

=-6x(2x-1)-22(2x-1)

=(2x-1)(-6x-22)

-2(2x-1)(3x+11)

multiply that -2 with (2x-1)

then U will get

(-4x+2)(3x+11)

: )
• 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)
• What if you end up with a binomial that are not the same, like at ? What do you do then?
• Doing the factoring by algebretic long division, I get x^3 + 5 + 8/x^3.
The remainder (8/x^3) shows that we are not overlooking a simpler solution.
• is there any other way to solve the problem besides writing it out?
• 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
• 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
• This might be a weird question but how would you solve for what f is??
• 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.