For this case we have the following xpresion:
[tex]2y ^ 2 + 3y + 4y + 6[/tex]
We can rewrite it as:
[tex]2y ^ 2 + 7y + 6[/tex]
Where:
[tex]a = 2\\b = 7\\c = 6\\[/tex]
We must factor, for this we follow the steps below:
Step 1:
The term of the medium must be rewritten as the sum of two terms, whose sum is 7 and the product is [tex]a.c = 2 * (6) = 12[/tex]:
Then, the term of the medium, fulfilling the two previous conditions, can be written as:
[tex]4y + 3y[/tex]
We check:
[tex]4 * 3 = 12\\4 + 3 = 7[/tex]
So, we have:
[tex]2y ^ 2 + 4y + 3y + 6[/tex]
Step 2:
The maximum common denominator (the largest integer that divides them without leaving residue) of each group is factored
[tex]2y ^ 2 + 4y + 3y + 6\\2y (y + 2) + 3 * (y + 2)[/tex]
Step 3:
We take common factor [tex](y + 2)[/tex]:
[tex](y + 2) (2y + 3)[/tex]
Thus, the expression [tex]2y ^ 2 + 3y + 4y + 6[/tex] can be factored as:
[tex](y + 2) (2y + 3)[/tex]
Answer:
[tex](y + 2) (2y + 3)[/tex]
