Question

Thực hiện phép tính theo hàng ngang:

a) (6x³ + 3x² + 4x + 2) : (3x² + 2)

b) (2x³ - 27x² + 115x - 150) : (x - 5)

c) (12x⁴ + 4x³ + 9x + 3) : (3x - 2)

d) (x⁵ + 4x³ + 3x² - 5x + 15) : (x³ - x + 3)

e) (3x⁵ - x⁴ - 2x³ + x² + 5) : (x² - 2x + 2)

g) (2x⁴ - 11x³ + 19x² - 20x + 9) : (x² - 4x + 1)

 

Answer 1

a) \(\left(6x^3+3x^2+4x+2\right):\left(3x^2+2\right)\)

\(=\left[3x^2\left(2x+1\right)+2\left(2x+1\right)\right]⋮\left(3x^2+2\right)\)

\(=\left[\left(3x^2+2\right)\left(2x+1\right)\right]⋮\left(3x^2+2\right)\)

\(=2x+1\)

b) \(\left(2x^3-22x^2-5x^2+60x+55x-150\right):\left(x-5\right)\)

\(=\left[\left(2x^3-22x^2+60x\right)-\left(5x^2-55x+150\right)\right]:\left(x-5\right)\)

\(=\left[2x\left(x^2-11x+30\right)-5\left(x^2-11x+30\right)\right]:\left(x-5\right)\)

\(=\left[\left(2x-5\right)\left(x^2-11x+30\right)\right]:\left(x-5\right)\)

\(=\left[\left(2x-5\right)\left(x^2-5x-6x+30\right)\right]:\left(x-5\right)\)

\(=\left[\left(2x-5\right)\left(x-5\right)\left(x-6\right)\right]:\left(x-5\right)\)

\(=\left(2x-5\right)\left(x-6\right)\)

\(=2x^2-17x+30\)

Answer 2

d) \(\left(x^5+4x^3+3x^2-5x+15\right):\left(x^3-x+3\right)\)

\(=\left(x^5+5x^3+3x^2-x^3-5x+15\right):\left(x^3-x+3\right)\)

\(=\left[\left(x^5-x^3+3x^2\right)+\left(5x^3-5x^2+15\right)\right]:\left(x^3-x+3\right)\)

\(=\left[x^2\left(x^3-x+3\right)+5\left(x^3-x^2+3\right)\right]:\left(x^3-x+3\right)\)

\(=\left[\left(x^2+5\right)\left(x^3-x+3\right)\right]:\left(x^3-x+3\right)\)

\(=x^2+5\)