Consider the monomials 15x^2, y^2, and 6x^3
a. Factor the monomials.
b. What factors of these monomials are common factors?
c. Find the greatest common factor of 15x^2, y^2, and 6x^3
The only common factor I see is 1
Are you sure you typed it correctly ? The y^2 appears to be an outlier.
Yea, I was confused about that too, I'm sure I typed it correctly.
Can someone please help me with this!
a. To factor the monomials, we need to break them down into their prime factors.
For 15x^2:
- The prime factorization of 15 is 3 * 5.
- The prime factorization of x^2 is x * x.
So, 15x^2 can be factored as 3 * 5 * x * x.
For y^2:
- The prime factorization of y^2 is y * y.
So, y^2 cannot be further factored since it is already in its simplest form.
For 6x^3:
- The prime factorization of 6 is 2 * 3.
- The prime factorization of x^3 is x * x * x.
So, 6x^3 can be factored as 2 * 3 * x * x * x.
b. To find the common factors, we need to compare the prime factorizations of the monomials.
The common factors will be the factors that are present in all three monomials.
From the prime factorizations:
- The common factors are 3, x, and x.
c. To find the greatest common factor (GCF), we need to find the highest power of each common factor that can be found in all three monomials.
From the common factors:
- The highest power of 3 that can be found in all three monomials is 3^1 = 3.
- The highest power of x that can be found in all three monomials is x^2.
Therefore, the greatest common factor of 15x^2, y^2, and 6x^3 is 3x^2.