divide using long division.
(6x^2+4x-16)/(2x-2)
first of all notice that each term divides by 2, so
(6x^2+4x-16)/(2x-2)
= (3x^2 + 2x-8)/(x-1)
hard to show the actual long division on here but you should get 3x+5 with a remainder of -3
a good long division site is
http://calc101.com/webMathematica/long-divide.jsp
To divide using long division, follow these steps:
Step 1: Ensure both the dividend (the expression being divided) and the divisor (the expression dividing the dividend) are arranged properly. Write the dividend and divisor in descending order of their exponents.
Given dividend: 6x^2 + 4x - 16
Given divisor: 2x - 2
Step 2: Begin the long division process by dividing the highest-degree term of the dividend (6x^2) by the highest-degree term of the divisor (2x). The result is the first term of the quotient.
6x^2 ÷ 2x = 3x
Step 3: Multiply the divisor (2x - 2) by the first term of the quotient (3x). Place the product underneath the dividend, aligning it according to the like terms.
3x
____________
2x - 2 | 6x^2 + 4x - 16
- (6x^2 - 6x)
_______________
10x - 16
Step 4: Subtract the product obtained in step 3 from the dividend. Write the result below the line.
3x
____________
2x - 2 | 6x^2 + 4x - 16
- (6x^2 - 6x)
_______________
10x - 16
Step 5: Bring down the next term of the dividend, which is the constant term (-16).
3x
____________
2x - 2 | 6x^2 + 4x - 16
- (6x^2 - 6x)
_______________
10x - 16
- (10x - 10)
_______________
-6
Step 6: Repeat steps 3 to 5 until there are no more terms to bring down or the degree of the resulting polynomial is lower than the divisor.
In this case, we have arrived at the end of the division since the degree of the resulting polynomial (-6) is lower than the divisor (2x - 2).
Step 7: The quotient is the result obtained from the division process.
The quotient is 3x - 6.
Therefore, (6x^2 + 4x - 16)/(2x - 2) = 3x - 6.