Question

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

Explanation:

Step1: Find GCF of coefficients

Coefficients: 30, 40, 51.
Factors of 30: 1,2,3,5,6,10,15,30
Factors of 40: 1,2,4,5,8,10,20,40
Factors of 51: 1,3,17,51
Greatest common factor (GCF) = 1

Step2: Check variable GCF

Terms have $x^2$, $xy$, $y^2$. No common variable across all terms.

Step3: Verify other statements

• First statement: No common $xy$ term, so false.
• Second statement: GCF is not $51x^2y^2$, false.
• Third statement: $10(3x^2+4xy+5y^2)=30x^2+40xy+50y^2

eq30x^2+40xy+51y^2$, false.

Answer:

The greatest common factor of the terms is 1.