Hello there. To solve this question using the AC method, we'll have to remember some properties about factorizing numbers.
Given the trinomial:
[tex]9z^2+15z+4[/tex]We start by labeling the numbers. The AC method requires that you find the A, B, C coefficients in:
[tex]Ax^2+Bx+C[/tex]In this case, it is easy to see that:
[tex]A=9,B=15,C=4[/tex]Now, we multiply A and C:
[tex]A\cdot C=9\cdot4=36[/tex]And we factorize this number in all the possible ways as a product of two numbers:
In the right column, you add the factors
And the numbers we'll choose are those that the sum is equal to B, in this case, 3 and 12 adds up to 15, that is the value of B we're looking for.
Now, we split the middle term in these factors:
[tex]9z^2+3z+12z+4[/tex]And we can factor some terms as follows:
[tex]\begin{gathered} 3z\cdot(3z+1)+4\cdot(3z+1) \\ (3z+4)(3z+1) \end{gathered}[/tex]This is the factorization of this trinomial.
