Factor completely.3, x, squared, plus, 14, x, minus, 53x 2 +14x−5

The expression you provided seems to have a typo. I believe you meant "3x^2 + 14x - 5". Here's how to factor it:

1. First, we need to find two numbers that multiply to (3*-5)=-15 and add to 14. Those numbers are 15 and -1.

2. Rewrite the middle term of the quadratic equation, splitting it into 15x - x:

   3x^2 + 15x - x - 5

3. Factor by grouping:

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

4. Notice that (x + 5) is a common factor:

   (3x - 1)(x + 5)

So, the factored form of 3x^2 + 14x - 5 is (3x - 1)(x + 5).

The expression you provided seems to be a bit unclear, but I'm assuming you're asking to factor the quadratic equation 3x^2 + 14x - 5.

Here are the steps to factor this equation:

1. First, we need to multiply the coefficient of x^2 (which is 3) by the constant term (which is -5). This gives us -15.

2. Next, we need to find two numbers that multiply to -15 and add to 14 (the coefficient of x). These numbers are 15 and -1 because 15 * -1 = -15 and 15 + -1 = 14.

3. We rewrite the middle term of the equation (14x) as the sum of 15x and -1x. This gives us 3x^2 + 15x - x - 5.

4. Now, we factor by grouping. The first two terms (3x^2 + 15x) can be factored to 3x(x + 5). The last two terms (-x - 5) can be factored to -1(x + 5).

5. Since the terms in parentheses are the same (x + 5), we can factor them out to get (3x - 1)(x + 5).

So, the factored form of the equation 3x^2 + 14x - 5 is (3x - 1)(x + 5).