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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.

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• 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 :)
• 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.
• 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
• 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.
• 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.
• What classifies as a quadratic expression? Can I just call anything a quadratic or are their some rules?
• A quadratic will is a polynomial with a degree of 2. You may see one in the form ax^2 + bx + c, or you may see it as two factors that each have an x: a(x-r)(x-s). An expression with a highest exponent of 3 would be called cubic, four would be called quartic, and so on.
• When I saw a+b=-3 I instantly went "it's -5+2" instead of 2-5. Does it matter which way? Can my a= -5 and b=2?
• Yes, you can use your numbers. You get the same factors.