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 each option

  • Option 1:
    • Expand (10(3x^{2}+4xy + 5y^{2})=30x^{2}+40xy+50y^{2}\neq30x^{2}+40xy + 51y^{2}).
  • Option 2:
    • If (30x^{2}+40xy + 51y^{2}=(ax + by+cz)\cdot xy=axy^{2}+bx^{2}y + cxy^{2}), which is not in the form of (30x^{2}+40xy + 51y^{2}).
  • Option 3:
    • The coefficients (30 = 2\times3\times5), (40=2^{3}\times5), (51 = 3\times17). There is no common factor among (30), (40) and (51) other than (1). Also, there is no common variable factor among the three terms ((x^{2}), (xy), (y^{2})) other than (1). So the greatest - common factor is not (51x^{2}y^{2}).
  • Option 4:
    • The coefficients (30 = 2\times3\times5), (40=2^{3}\times5), (51 = 3\times17). There is no common factor among (30), (40) and (51) other than (1). For the variables, the first term has (x^{2}), the second has (xy) and the third has (y^{2}). The greatest common variable factor is (1). So the greatest common factor of the terms is (1).

Answer:

The greatest common factor of the terms is 1.