which statement is true about the factorization of $30x^{2}+40xy + 51y^{2}$?\nthe polynomial can be…

which statement is true about the factorization of $30x^{2}+40xy + 51y^{2}$?\nthe polynomial can be rewritten after factoring as $10(3x^{2}+4xy + 5y^{2})$.\nthe polynomial can be rewritten as the product of a trinomial and $xy$.\nthe greatest common factor of the polynomial is $51x^{2}y^{2}$.\nthe greatest common factor of the terms is 1.

which statement is true about the factorization of $30x^{2}+40xy + 51y^{2}$?\nthe polynomial can be rewritten after factoring as $10(3x^{2}+4xy + 5y^{2})$.\nthe polynomial can be rewritten as the product of a trinomial and $xy$.\nthe greatest common factor of the polynomial is $51x^{2}y^{2}$.\nthe greatest common factor of the terms is 1.

Answer

Explanation:

Step1: Analyze coefficients

The coefficients of the polynomial $30x^{2}+40xy + 51y^{2}$ are 30, 40, and 51. Find the greatest - common factor of 30, 40, and 51. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. The factors of 51 are 1, 3, 17, 51. The greatest common factor of 30, 40, and 51 is 1.

Step2: Analyze variables

For the variable part, the first term has $x^{2}$, the second term has $xy$, and the third term has $y^{2}$. There is no common variable factor other than 1 for all three terms.

Answer:

The greatest common factor of the terms is 1.