Question

(x^4 + 2x^3 + 10x - 25):(x^2 +5)

Answer 1

\(\frac{x^4+2x^3+10x-25}{x^2+5}\)

\(=\frac{\left(x^4+5x^2\right)+\left(2x^3+10x\right)-\left(5x^2+25\right)}{x^2+5}\)

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

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

\(=x^2+2x-5\)\(\left(x^2+5\ne0\right)\)

Tham khảo nhé~

Answer 2

      \(x^4+2x^3+10x-25\)

\(=x^4+5x^2+2x^3+10x-5x^2-25\)

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

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

Vậy \(\left(x^4+2x^3+10x-25\right):\left(x^2+5\right)=x^2+2x-5\)