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:

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