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## Algebra 1

### Course: Algebra 1>Unit 13

Lesson 9: Strategy in factoring quadratics

# Strategy in factoring quadratics (part 1 of 2)

There are a lot of methods to factor quadratics, which apply on different occasions and conditions. After learning all of them in separate, let's think strategically about which method is useful for a given quadratic expression we want to factor.

## Want to join the conversation?

• Have we found all possible strategies for factoring? Or is that even possible?
• Considering modern math, we might have, but there could also be more efficient ways of doing this other than "guess and check". Hopefully we will find more efficient ways!
• At Sal shows the "perfect square" techinque. Is it possible to factor a perfect square when the constant is negative. For example, 3x^2+30x-75?
• No. The reason why we can't is because that would require the second term of the square (the b in `(a+b)^2`) to be a negative number when squared. Although this is possible if b is a complex (or imaginary) number, factoring usually only uses real numbers. The square of any real number is always positive (try it: A x A is always positive), so the last term cannot be negative.

There is one major exception: If the leading coefficient (the 3 in your example) is also negative, then when you factor it out, the constant term will become positive (because a negative number divided by a negative number results in a positive number) and you can factor it out normally.

If this was confusing or you still have questions, feel free to comment them below and I'll try my best to answer them!

Hope this helps!
• Please excuse my naivety , but what is the purpose of factoring?? How does it help??
• It will give you the x intercepts of the quadratic if there are any.
• So when you add -12 and 1 you get -11, and when you add -1 and 12 you get 11, does this mean it will always be that way? Or are there times when that doesn't happen?
• it will always be that way, check out the lessons on positive negative numbers to get the intuition behind it.
• I factored "3x^2 + 30x + 75" and I got (3x + 15)(x + 5).
Do we have multiple answers? Am I wrong?
• Well, you could have factored a 3 in the beginning to get 3(x^2 + 10x + 25) which is a perfect square 3(x+5)^2. So you have two answers, x = -5 and x = -5, but they are the same, so there is only one unique answer.
• Hi, when you are doing the a+b and a.b shoudn't you find -b/a and c/a respectively?
Thanks.
• can we also factor the 6x^2+3x
like this 6(x^2+3x)
6(x(x+3))
• No, that does not work because when you distribute, you will get 6x^2+18x. The right way to factor it is by taking the greatest common factor out, which is 3x. It would be 3x(2x+1).
• Has anyone taken the algebra 1 EOC?
I'm terrified!!