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Factoring algebra Video transcript We're told to factor 4x to the fourth y, minus 8x to the third y, minus 2x squared. So to factor this, we need to figure out what the greatest common factor of each of these terms are.
So let me rewrite it. So we have 4x to the fourth y, and we have minus 8x to the third y, and then we have minus 2x squared. So in the other videos, we looked at it in terms of breaking it down to its simplest parts, but I think we have enough practice now to be able to do a little bit more of it in our heads.
So what is the largest number that divides into all of these? When I say number I'm talking about the actual, I guess, coefficients. We don't have to worry about the negative signs just yet. And we say, well, the largest, of, the largest common factor of 2, 8 and 4 is 2.
So that is the largest number that's going to be part of the greatest common factor.
So let's write that down. So it's going to be 2. And then what's the greatest, I guess, factor, what's the greatest degree of x that's divisible into all three of these? Well, x squared goes into all three of these, and obviously that's the greatest degree of x that can be divided into this last term.
So x squared is going to be the greatest common x degree in all of them.
And then what's the largest degree of y that's divisible into all of them? Well, these two guys are divisible by y, but this guy isn't, so there is no degree of y that's divisible into all of them. So the greatest common factor of all three of these guys right here is 2x squared. So what we can do now is we can think about each of these terms as the product of the 2x squared and something else.
And to figure that something else we can literally undistribute the 2x squared, say this is the same thing, or even before we undistribute the 2x squared, we could say look, 4x to the fourth y is the same thing as 2x squared, times 4x to the fourth y, over 2x squared.
If you just multiply this out, you get 4xy. Similarly, you could say that 8x to the third y-- I'll put the negative out front-- is the same thing as 2x squared, our greatest common factor, times 8x to the third y, over 2x squared. And then finally, 2x squared is the same thing as if we factor out 2x squared-- so we have that negative sign out front-- if we factor out 2x squared, it's the same thing as 2x squared, times 2x squared, over 2x squared.Expression Factoring Calculator.
Expression: Example Expression. Hint: Use the equation At this point the calculator will attempt to factor the expression by dividing a GCF, and identifying a difference between two squares, or factorable trinomials. Use the following rules to enter expressions into the calculator. The quantity a n is called the order-n residue of such a p-adic integer.
An ordinary integer N (also called a rational integer in this context) is a special case of a p-adic integer, whose order-n residue is simply N mod p n.. The sum (or the product) of two p-adic integers is defined as the p-adic integer whose order-n residue is the sum (or the product) of the order-n residues of both operands.
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4. A quantity by which a stated quantity is multiplied or divided, so as to indicate an increase or decrease in a measurement: The rate increased by a factor of ten.
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