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How Do You Find the Factors of a Monomial?

Write 4x2y5 in factored form

Summary

  1. Our factors are 4, x2, and y5
  2. 4 is a constant
  3. x2 and y5 are variables
  4. 4 factors into 2•2
  5. x2 has a degree of 2
  6. y5 has a degree of 5
  7. Instead of writing 4, write 2•2
  8. Instead of writing x2, write x•x
  9. Instead of writing y5, write y•y•y•y•y

Notes

    1. The factors are what is being multiplied together
    1. We need to determine which of our factors are constants and which are variables
    1. 4 is a number that doesn't change, so it is a constant
    1. x2 and y5 can have any value, so they are variables
    1. Remember, the constant was 4
    1. 2 and 2 are 4's prime factors
    1. Remember, our variables were x2 and y5
    1. The degree is just the value of the exponent
    2. So the degree of x2 is 2
    1. The degree is just the value of the exponent
    2. So the degree of y5 is 5
    1. Now that we have all the prime factors, we just need to write them out
    1. The first factor in our monomial was 4
    2. Its prime factors are 2 and 2
    1. x2 is the same as x•x
    1. x2's prime factors are x and x
    1. y5 is the same as y•y•y•y•y
    1. y5 factors into y•y•y•y•y