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Rewrite [tex]$6x^2 + 2xy + 9x + 3y$[/tex] in factored form.

A. [tex]$(2x+3)(3x+y)$[/tex]
B. [tex][tex]$(2x+y)(3x+3)$[/tex][/tex]
C. [tex]$(3x+2)(3x+y)$[/tex]
D. [tex]$(3x+y)(2x+1)$[/tex]

Sagot :

GinnyAnsweridn
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].
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