Question

Factor........................

Answer 1

For this case we have a quadratic polynomial given by:

`6x ^ 2-7x-5`

Where:

`a = 6\\b = -7\\c = -5`

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
`a.c = 6 * (- 5) = - 30`:

Then, the term of the medium, fulfilling the two previous conditions, can be written as:

`-10x + 3x`

We check:

`-10 * 3 = -30\\-10 + 3 = -7`

So, we have:

`6x ^ 2-10x + 3x-5`

Step 2:

The maximum common denominator (the largest integer that divides them without leaving residue) of each group is factored

`6x ^ 2-10x + 3x-5\\2x (3x - 5) + 1 * (3x - 5)`

Step 3:

We take common factor
`(3x - 5)`:

`(3x - 5) (2x + 1)`

Thus, the expression
`6x^2-7x-5`can be factored as:

`(3x - 5) (2x + 1)`

Answer:

`(3x - 5) (2x + 1)`