Question

Using division, what is the quotient (2x3 - 2x - 12) ÷ (x - 2)?

2x² + 4x-6 +
2x² - 4x + 6
1
X 2)

Answer 1

Answer: 2x²+4x+6

Explanation:

`\displaystyle\\(2x^3-2x-12)/(x-2) =\\\\(2(x^3-x-6))/(x-2)=\\\\ (2(x^2-8+8-x-6))/(x-2) =\\\\(2(x^3-2^3-x+2))/(x-2) =\\\\(2((x^3-2^3)-(x-2)))/(x-2)=\\\\(2((x-2)(x^2+2x+2^2)-(x-2)))/(x-2) =\\\\(2(x-2)(x^2+2x+4-1))/(x-2)=\\\\2(x^2+2x+3)=\\\\2x^2+4x+6`