Answer:
The quotient is (10x - 5) and the reminder is -50 ⇒ 1st answer
Explanation:
* Lets solve the long division by easiest way
∵ (10x² - 85x - 10)/(x - 8)
∵ (10x² - 85x - 10) is the dividend
∵ (x - 8) is the divisor
- Divide the first term of the dividend by the first term of the divisor
∴ 10x² ÷ x = 10x ⇒ first term of the quotient
- Multiply 10x by the the divisor
∴ 10x(x - 8) = 10x² - 80x
- Subtract the answer from the dividend
∴ (10x² - 85x - 10) - (10x² - 80x) =
# 10x² - 10x² = 0
# -85x - -80x = -85x + 80x = -5x
# -10
∴ (10x² - 85x - 10)/(x - 8) = 10x + (-5x - 10)/(x - 8)
* Repeat the same steps again with the new dividend -5x - 10
- Divide the first term of the dividend by the first term of the divisor
∴ -5x ÷ x = -5 ⇒ second term of the quotient
- Multiply -5 by the divisor
∴ -5(x - 8) = -5x + 40
- Subtract the answer from the dividend
∴ (-5x - 10) - (-5x + 40) =
# -5x - -5x = -5x + 5x = 0
# -10 - 40 = -50
∴ (-5x - 10)/(x - 8) = -5 + -50/(x - 8)
∴ (10x² - 85x - 10)/(x - 8) = 10x - 5 + -50/(x - 8)
- The quotient is the answer of the division
∴ The quotient is (10x - 5) and the reminder is -50