divide (12x^3-26x^2-34x-8)/(6x+2)

is it

2x^2 -5x-4?

nope

To divide the polynomial (12x^3 - 26x^2 - 34x - 8) by (6x + 2), we can use long division method. Here's how you can get the answer:

Step 1: Arrange the polynomial in descending order of powers of x:
12x^3 - 26x^2 - 34x - 8

Step 2: Divide the first term of the polynomial (12x^3) by the first term of the divisor (6x). The result will be the first term of the quotient:
Quotient: 2x^2

Step 3: Multiply the divisor (6x + 2) by the first term of the quotient (2x^2), and subtract the result from the polynomial:
(12x^3 - 26x^2 - 34x - 8) - (2x^2 * (6x + 2))

Simplifying this expression gives us:
12x^3 - 26x^2 - 34x - 8 - (12x^3 + 4x^2)
= -30x^2 - 34x - 8

Step 4: Bring down the next term from the polynomial (-30x^2), and repeat steps 2 and 3 until all terms have been divided:

-30x^2 divided by 6x (from the divisor) gives -5x.
Multiply -5x by (6x + 2) and subtract the result from the polynomial:
-30x^2 - (-5x * (6x + 2))
Simplifying gives: -30x^2 - (-30x^2 - 10x)
= 10x

Next, bring down the next term from the polynomial (-34x):
The new polynomial becomes: 10x - 34x - 8

Step 5: Repeat steps 2 and 3:

-34x divided by 6x gives -5.6667 (rounded to 5 decimal places)
Multiply -5.6667 by (6x + 2) and subtract the result from the polynomial:
-34x - (-5.6667 * (6x + 2))
Simplifying gives: -34x + 34x + 11.3333
= 11.3333

Finally, bring down the last term from the polynomial (-8):
The new polynomial becomes: 11.3333 - 8

Step 6: There are no more terms to bring down, so the division is complete. The quotient is the sum of all the terms we obtained earlier:
Quotient: 2x^2 - 5x + 11.3333

Therefore, the division of (12x^3 - 26x^2 - 34x - 8) by (6x + 2) yields a quotient of 2x^2 - 5x + 11.3333.