2x^3+3x^2-5x-6=0

Factor out x+1

To factor out x+1 from the given equation, you can use synthetic division or long division.

Here's how you can do it using synthetic division:

Step 1: Set up the synthetic division table:
-1 | 2 3 -5 -6

Step 2: Bring down the first coefficient, which is 2:
-1 | 2

Step 3: Multiply the number you brought down by the divisor (-1) and write the result below the next coefficient:
-1 | 2
-2

Step 4: Add the numbers in the second row:
-1 | 2 3 -5 -6
-2

Step 5: Multiply the previous number (-2) by the divisor (-1) and write the result below the next coefficient:
-1 | 2 3 -5 -6
-2 1

Step 6: Add the numbers in the second row:
-1 | 2 3 -5 -6
-2 1 -6

The final row represents the coefficients of the quotient when x is divided by x+1. The last number in the bottom row, -6, is the remainder.

So, using synthetic division, we have:

2x^3 + 3x^2 - 5x - 6 = (x+1)(2x^2 + x - 6)

Now, you can factor out the quadratic term 2x^2 + x - 6 further if needed.