(x^2 - 8x + 6)/(x + 2)
= x - 10 + ((26)/(x + 2))
To solve the given expression, (x^2 - 8x + 6)/(x + 2), using long division, you can follow these steps:
Step 1: Divide the first term of the numerator (x^2) by the first term of the denominator (x):
(x^2)/(x) = x
Step 2: Multiply the entire denominator (x + 2) by the result from step 1 (x):
x * (x + 2) = x^2 + 2x
Step 3: Subtract the result obtained in step 2 from the numerator (x^2 - 8x + 6):
(x^2 - 8x + 6) - (x^2 + 2x) = -8x - 2x + 6
Step 4: Bring down the next term from the original numerator (6):
-8x - 2x + 6
Step 5: Divide the first term of the new numerator (-8x) by the first term of the denominator (x):
(-8x)/(x) = -8
Step 6: Multiply the entire denominator (x + 2) by the result from step 5 (-8):
-8 * (x + 2) = -8x - 16
Step 7: Subtract the result obtained in step 6 from the new numerator (-8x - 2x + 6):
(-8x - 2x + 6) - (-8x - 16) = -2x + 6 + 8x + 16
Step 8: Simplify the terms in the new numerator:
-2x + 6 + 8x + 16 = 6x + 22
Finally, the quotient is x - 10 + ((26)/(x + 2)).