Lesson 93 – Doodles Do Algebra

lesson93doodlecatcToday your child learns to find the greatest common divisor between two polynomials. The method is called the Euclidian Algorithm, but that part is not very important for your child. He just needs to learn how to do it.

There are 3 rules:

1. Divide the larger polynomial by the smaller one.

2. Ignore any factors of one polynomial if they are not common to the other polynomial. Unique factors are meaningless to finding the greatest common factor

3. Reserve the quantities of the greatest common factor as you find them during the division process.

The overall general idea is much the same – it is a matter of reducing each polynomial to its prime factors and then comparing, just a bit more complex since we are dealing with polynomials.

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Answers:

1. First figure out which polynomial is the larger one. 5a^2+5ax is definitely larger than a^2-x^2 because the first polynomial adds to 5 times the square of a and the second polynomial subtracts from the square of a (this is assuming a will be a positive number).

Second ignore factors of the smaller polynomial that are not common to the larger one. The first polynomial has factors 5, a, and (a+x). The second polynomial has factors (a+x) and (a-x). So we ignore the 5 and a.

Third step: the greatest common divisor between the two polynomials is then (a+x) because that is the common prime.

2. First figure out which polynomial is largest: in this case it is x^2+2cx+c^2 because the other polynomial subtracts a quantity.

Second, ignore the factors of one polynomial not common to the other. The first polynomial, x^2+2cx+c^2 , has factors which are (x+c), and (x+c). The second polynomial, x^3-c^2x , has factors x, (x+c), and (x-c).

So finally, the greatest common divisor is (x+c).

3. First, the largest of the two polynomials is x^2+5x-6.

Second, the first polynomial, x^2+5x-6, has factors which are (x+6), and (x-1). The second polynomial, x^2+2x-3, has factors which are (x+3), and (x-1).

So finally, the greatest common divisor is (x-1).

See, it is not too hard if you just keep the overall idea in mind and work the steps.

 doodlemom