Question

Sắp xếp các đa thức rồi làm tính chia:

a) (15 + 5x² - 3x³ - 9x) : (5 - 3x)

b) (x⁴ - 2x³ - 1 + 2x) : (x² - 1)

Answer 1

a) Ta có: \(\frac{15+5x^2-3x^3-9x}{5-3x}\)

\(=\frac{-3x^3+5x^2-9x+15}{5-3x}\)

\(=\frac{3x^3-5x^2+9x-15}{3x-5}\)

\(=\frac{x^2\left(3x-5\right)+3\left(3x-5\right)}{3x-5}\)

\(=\frac{\left(3x-5\right)\left(x^2+3\right)}{3x-5}\)

\(=x^2+3\)

b) Ta có: \(\frac{x^4-2x^3-1+2x}{x^2-1}\)

\(=\frac{x^4-2x^3-1+2x}{x^2-1}\)

\(=\frac{\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)}{x^2-1}\)

\(=\frac{\left(x^2-1\right)\left(x^2+1-2x\right)}{x^2-1}\)

\(=x^2-2x+1=\left(x-1\right)^2\)