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### Course: Algebra basics>Unit 7

Lesson 5: Factoring quadratics 1

# Factoring quadratics as (x+a)(x+b)

Sal factors x²-3x-10 as (x+2)(x-5) using the sum-product form: (x+a)(x+b)=x²+(a+b)x+a*b.

## Want to join the conversation?

• Will it ever happen that a and b are going to be decimals?
• Yes. It is possible.

Also, if you have a fraction, it can be transformed to decimal. They're just different representations of the same quantity. :)
• I know that when you have something like 7(x^2 + 5) + 6y(x^2 + 5), it can become (6y + 7)(x^2 + 5), but why?
• I have an easy way for you to visualize this, although I know you asked this 3 years ago and are probably smarter than me now but anyways:
Since x^2 + 5 = x^2 + 5
Let's assign the quantity (x^2 + 5) some variable, say, z.
Therefore 7(z) + 6y(z)
Reverse distribute the z and you get z(7+6y)
And then substitute (x^2 + 5) back in for z
(x^2 + 5)(7 + 6y)

Hope that helps :)
• Why is the word quadratic used? Just curious!
• The word quadratic comes from the latin word for square, and this is because in a quadratic, the highest degree is x^2
• i need an explainsion for dummies
• I love how you say it, it makes me feel less dumb
• How would this work if there ISN'T two numbers that add, subtract, multiply and divide into the desired numbers?
• Then if you decided that the expression is already in simplest form, then it shall be considered unfactorable.
• When the resulting binomials have a positive and a negative number, why does it matter which one's negative and which one's positive? I saw somewhere on this site that suggests that the larger number is always the negative, but when I employ that in practice here, your program says I'm wrong (until I change the negative to the smaller number, instead.) Thanks in advance.
• The placement of the signs does matter!
The rule of thumb is that the larger number gets the sign of the original middle term.
Consider: x^2 -3x -10
We need factors of -10 that add to -3
Factors of -10 would be: 2(-5) or -2(5)
Only one set will create the -3 when you add the 2 numbers. Since this is a minus 3, the larger number needs the minus sign. So, you want: 2(-5).
Of course, you can also check this by just adding: 2 + (-5) = -3 (this works). While -2 + 5 = +3 (this doesn't work).

Once you have selected the 2 numbers, use those numbers and their respective signs in your factors: (x+2)(x-5)

Hope this helps.
• How could you tell that the bigger number is negative in the video?...
• Sal is factoring x^2-3x-10. So, he finds two numbers that:
1) Multiply to -10 (the last term)
2) Add to -3 (the middle term)

The -10, tells us that one number must be positive and the other negative to get a negative number after multiplying (from basic rules for multiplying signed numbers).

So, you will add a positive number and a negative number to create the -3. The rules for adding numbers with different signs tells us that the dominant number (the one furthest from 0) will create the final sign. Thus, the larger of the two numbers must carry be negative in order to get -3 as a result.

If you aren't sure, just check the options.
2-5 = -3
-2+5 = +3

Hope this helps.
• Before now we were told that equations in the form of ax^2+bx+c were polynomials 'in standard form'. Now we are hearing the word quadratic - introduced for the first time I think? What are the minimum requirements for an equation to be 'quadratic'?
• A "quadratic" is a polynomial where the highest power is "2". They show up so often, that it's useful to have a separate name for that kind of polynomial.
• I understand this explanation but I just wanted to know if there's a quicker way to do this or is this the quickest way?
• This is the quick way, he spent a long time for a process that will be much quicker when you practice. The basic question is what two numbers multiply to be c and add to be b?
There are other hints that might make more sense of it such as noticing the signs of b and c that can help decide the best places to start.
If C is positive, the sign of B will give us the two signs of the factors, so we add to get B (that way I do not care if they are both negative or both positive)
If C is negative, they are opposite signs and B tells the sign of the biggest, so we subtract and follow put the biggest number with the sign of B.