Question

(12x^3 - 2x^2 - 12x + 3) ÷ (4x+2)
find quotient
find remainder

Answer 1

quotinet = 3x² - 2x - 2

remainder = 7

Explanation:

12x³ - 2x² - 12x + 3

= 3x²(4x + 2) - 6x² - 2x² - 12x + 3

= 3x²(4x + 2) - 8x² - 12x + 3

= 3x²(4x + 2) - 2x(4x + 2) + 4x - 12x + 3

= 3x²(4x + 2) - 2x(4x + 2) - 8x + 3

= 3x²(4x + 2) - 2x(4x + 2) - 2(4x + 2) + 4 + 3

= 3x²(4x + 2) - 2x(4x + 2) - 2(4x + 2) + 7

= (4x + 2)(3x² - 2x - 2) + 7

so

quotinet = 3x² - 2x - 2

remainder = 7