Some questions about math factor proves

  • Thread starter furtivefelon
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In summary, the conversation discusses three different math factor proofs that the speaker is struggling to figure out. The first proof involves showing that x-y is a factor of x^n-y^n, and the speaker has found that the other factor is x^(n-1) + x^(n-2)y + x^(n-3)y^2 + ... + y^(n-1). The second proof involves proving that (x+a) is a factor of (x+a)^5 + (x+c)^5 + (a-c)^5, and the third proof involves proving that (x-a) is a factor of x^3 - (a+b+c)x^2 + (ab+bc+ca)x - abc. The conversation
  • #1
furtivefelon
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hi, i have three math factor proves i can't figure out:

1. Show that x-y is a factor of x^n-y^n
Through empircal testing, i figured out the other factor must be x^(n-1) + x^(n-2)y + x^(n-3)y^2 + ... + y^(n-1), though i can't come up with a prove for it..

2. Prove that (x+a) is a factor of (x+a)^5 + (x+c)^5 + (a-c)^5

3. prove that (x-a) is a factor of x^3 - (a+b+c)x^2 + (ab+bc+ca)x - abc

the last two i have no idea where to begin.. Can someone please help me? thanks :D
 
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  • #2
Try this: (x- a) is a factor of polynomial p(x) if and only if p(a)= 0.

What happens if you put x= a in each of those polynomials?
 
  • #3
x^(n-1) + x^(n-2)y + x^(n-3)y^2 + ... + y^(n-1), though i can't come up with a prove for it..

Well, what do you get when you multiply this by (x - y)? If you get x^n - y^n, then you have a proof! (not a 'prove')
 

What is a math factor proof?

A math factor proof is a method used to show that a number is divisible by another number. It involves breaking down the number into its prime factors and showing that the other number can be divided evenly into those factors.

Why is math factor proof important?

Math factor proofs are important because they provide a way to prove the divisibility of numbers, which is a fundamental concept in mathematics. They also help in simplifying fractions and finding the greatest common factor of two or more numbers.

What are some common strategies used in math factor proofs?

Some common strategies used in math factor proofs include prime factorization, finding common factors, using the division algorithm, and using the fundamental theorem of arithmetic.

Can math factor proofs be used for non-integer numbers?

Yes, math factor proofs can be used for non-integer numbers as well. In this case, the numbers are broken down into their prime factors and the proof is based on the divisibility of those factors.

Are there any online resources for learning more about math factor proofs?

Yes, there are many online resources available for learning more about math factor proofs. Some recommended websites include Khan Academy, MathisFun, and Math Planet, which offer tutorials and practice problems for all levels of math factor proofs.

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