For this case we have a quadratic polynomial given by:
[tex]6x ^ 2-7x-5[/tex]
Where:
[tex]a = 6\\b = -7\\c = -5[/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 = 6 * (- 5) = - 30[/tex]:
Then, the term of the medium, fulfilling the two previous conditions, can be written as:
[tex]-10x + 3x[/tex]
We check:
[tex]-10 * 3 = -30\\-10 + 3 = -7[/tex]
So, we have:
[tex]6x ^ 2-10x + 3x-5[/tex]
Step 2:
The maximum common denominator (the largest integer that divides them without leaving residue) of each group is factored
[tex]6x ^ 2-10x + 3x-5\\2x (3x - 5) + 1 * (3x - 5)[/tex]
Step 3:
We take common factor [tex](3x - 5)[/tex]:
[tex](3x - 5) (2x + 1)[/tex]
Thus, the expression [tex]6x^2-7x-5[/tex]can be factored as:
[tex](3x - 5) (2x + 1)[/tex]
Answer:
[tex](3x - 5) (2x + 1)[/tex]
