Question: Exponents and Polynomials Greatest common factor of three univariate monomials Find the greatest…

Exponents and Polynomials

Greatest common factor of three univariate monomials

Find the greatest common factor of these three expressions.

\(10y^2\), \(35y^5\), and \(30\)

Solution

To find the greatest common factor (GCF) of the expressions \(10y^2\), \(35y^5\), and \(30\), we need to follow these steps: First, find the GCF of the numerical coefficients: 10, 35, and 30. The prime factorizations are: \[ 10 = 2 \times 5 \] \[ 35 = 5 \times 7 \] \[ 30 = 2 \times 3 \times 5 \] The only common factor is 5. Next, consider the variable \(y\). The smallest power of \(y\) present in the expressions is \(y^0\) (since 30 has no \(y\)), so no \(y\) can be a part of the GCF. Therefore, the GCF of \(10y^2\), \(35y^5\), and \(30\) is: \[ 5 \]