Answer:
[tex]4*(x-9)*(x+2)[/tex]
Step-by-step explanation:
Start by extracting the numerical common factors. Notice that 4 is a factor in all coefficients. Therefore: [tex]4x^2-28x-72=4(x^2-7x-18)[/tex]
Now study the trinomial that is left, and look for numerical coefficients that multiplied give as result the last coefficient in the trinomial (-18) and when combined give you the coefficient in the linear term (-7). Notice that the coefficient -18 can be created by the product of (-9) times (2), and that these numbers combined give you exactly "-7" which is your middle coefficient. Therefore use them to factor out the trinomial:
[tex]x^2-7x-18=x^2-9x+2x-18=\\=x^2-9x+2(x-9)=x(x-9)+2(x-9)=\\=(x-9)*(x+2)[/tex]
Therefore, the full factoring of the initial trinomial is written as: [tex]4*(x-9)*(x+2)[/tex]
