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# Factoring completely with a common factor

We can factor quadratics by first pulling out a common factor so the result looks like a(x+b)(x+c). Created by Sal Khan.

## Want to join the conversation?

• Does a have to be greater than b when a≠b? For example, 8(x+2)(x+4) versus 8(x+4)(x+2).
• I didn't really understand what you were asking, but 8(x+2)(x+4) and 8(x+4)(x+2) are exactly the same thing. Remember that the order in which you multiply two or more things together doesn't change the final product.
a*b*c = b*a*c = c*a*b

Hope this helps.
• To use this method does a have to be greater than 1?
• It doesn't need to be greater than 1, but if it wasn't greater than 1 then it would be pointless. If the only greatest common factor was 1 for the expression, then you can't really factor the expression therefore making the expression prime.
• How do I do this with numbers that have no common factors? My maths teacher says it is possible but I do not understand how.
• How do I know if my (ax) factor should be factored out positively or negatively? At he goes from positive to negative.
• Think about it. When you're factoring -3, you're essentially dividing all terms by -3 and then multiplying that -3 again. So, divide -3x^2 by -3. You get x^2. Then, divide +21x by -3. You get -7x. Finally, divide -30 by -3. You get 10. That's how you factor it out.

• in shouldn't be 4((x-3)*(x+1))? i'm thinking:
4(x-3)*(x+1)
(4x-12)*(x+1)
4x^2-8x-12

also, i found strange how in the alternative path of the second example "3(-x^2+7x-10)". it seem like there is no answer to: a+b=7; a*b=-10. did i miss something?
• At Sal says that you can factor the thing(what should I call it? A trinomial multiplied by a constant), he says you can factor with the "x squared" being negative. So how can you factor the trinomial with the x squared leading term being negative? Thank you.
-3x^2+21x-30 = (-3x+6)(x-5)
Find 2 number that gives 90 when multiplied and 21 when added.
15 and 6
-3x^2+15x+6x-30
-3x(x-5)+6(x-5)
(-3x+6)(x-5)
Is this still correct?
When checked it still gives me the first -3x^2+21x-30. But the final answer way different than the one shown in the video
• You are correct, but yours is not the completely factored form of this polynomial. Sal factors out 3 at the very beginning, and you can see this in yours: in -3x+6, 3 is common.

Hope this helps.
• How do we 'reverse' the process? eg at , how do we apply the distributive property to end up with the original trinomial 4x^2-8x-12? Does the 4 multiply just the first set of brackets or both of them ? i.e. 4(x-3) and 4(x+1) or 4(x-3) and (x+1) remains as it is before expanding?