Question

Which statement is true about the factorization of 30x2+40xy+51y2

Answer 1

The complete question is
Which statement is true about the factorization of 30x² + 40xy + 51y²?

A. The factorization of the polynomial is 10(3x2 + 4xy + 5y2).
B. The polynomial can be rewritten as the product of a trinomial and xy.
C. The greatest common factor of the polynomial is 51x2y2.
D. The polynomial is prime, and the greatest common factor of the terms is 1.

we know that

case A) is not right because 10 is not a common factor of the three terms.
case B) is not right because the original polynomial is already a trinomial
case C) is not right because the terms do not contain 51x^2y^2
case D) is right 
because
Factors of 30 are-----> 1,2,3,5,6,10,15,30
Factors of 40 are-----> 1,2,4,5,8,10,20,40
Factors of 51 are-----> 1,51
so
The "Greatest Common Factor" is the largest of the common factors
the GFC is 1

therefore

the answer is the option
D. The polynomial is prime, and the greatest common factor of the terms is 1