Greatest common divisor of two polynomials
Okay, imagine you have two big piles of Legos, one pile has red, blue, and green Legos, and the other pile has red, white, and yellow Legos. You want to find the biggest pile of Legos that you can make using only the Legos that are in both piles. That biggest pile is called the greatest common pile of Legos.
Now, instead of Legos, we have polynomials. Polynomials are just fancy math equations with different levels of powers like x or x² or x³. So, we have two piles of polynomials, one has x² + 2x + 1, and the other has x² - x - 2. We want to find the biggest polynomial that we can make using only the polynomials that are in both piles. That biggest polynomial is called the greatest common divisor of the two polynomials.
To find it, we basically have to break down both polynomials into their factors, which are the different parts that we can multiply together to get the original polynomial back. So for the first polynomial, x² + 2x + 1, the factors are (x+1) and (x+1) again. For the second polynomial, x² - x - 2, the factors are (x-2) and (x+1).
Now, we look to see which factors are the same in both polynomials. In this case, we see that (x+1) is a factor in both polynomials. So, we can say that the greatest common divisor of x² + 2x + 1 and x² - x - 2 is (x+1).
That's basically it! We just have to find the factors and see which ones are the same in both polynomials. Then, we can say that the biggest polynomial we can make with those factors is the greatest common divisor of the two polynomials.
Now, instead of Legos, we have polynomials. Polynomials are just fancy math equations with different levels of powers like x or x² or x³. So, we have two piles of polynomials, one has x² + 2x + 1, and the other has x² - x - 2. We want to find the biggest polynomial that we can make using only the polynomials that are in both piles. That biggest polynomial is called the greatest common divisor of the two polynomials.
To find it, we basically have to break down both polynomials into their factors, which are the different parts that we can multiply together to get the original polynomial back. So for the first polynomial, x² + 2x + 1, the factors are (x+1) and (x+1) again. For the second polynomial, x² - x - 2, the factors are (x-2) and (x+1).
Now, we look to see which factors are the same in both polynomials. In this case, we see that (x+1) is a factor in both polynomials. So, we can say that the greatest common divisor of x² + 2x + 1 and x² - x - 2 is (x+1).
That's basically it! We just have to find the factors and see which ones are the same in both polynomials. Then, we can say that the biggest polynomial we can make with those factors is the greatest common divisor of the two polynomials.
Related topics others have asked about: