Sure! Let's factor the polynomial expression [tex]\(6x^2 + 2xy + 9x + 3y\)[/tex].
To start, we need to look at the given polynomial and identify a way to factor it into a product of two binomials. The aim is to rewrite it in one of the provided factored forms.
Given the expression:
[tex]\[6x^2 + 2xy + 9x + 3y,\][/tex]
we want to write it in a factored form such as:
[tex]\[(Ax + B)(Cx + D).\][/tex]
We need to determine the correct coefficients that match one of the expressions provided. After factoring [tex]\(6x^2 + 2xy + 9x + 3y,\)[/tex] we achieve:
[tex]\[(2x + 3)(3x + y).\][/tex]
So, the polynomial [tex]\(6x^2 + 2xy + 9x + 3y\)[/tex] factors to [tex]\((2x + 3)(3x + y)\)[/tex]. This corresponds to the first option given in the list:
[tex]\[(2x + 3)(3x + y).\][/tex]
Therefore, the factored form of the polynomial [tex]\(6x^2 + 2xy + 9x + 3y\)[/tex] is [tex]\((2x + 3)(3x + y)\)[/tex].
