Question

B1: Làm phép chia:

a) (x^4+x^3+6x^2+5x+5):(x^2+x+1)

b) (x^4+x^3+2x^2+x+1):(x^2+x+1)

c) (3x^3+8x^2-x-10):(3x+5)

B2: Xác định hệ số a, sao cho:

a) (a^3x^3+3ax^2-6x-2a) chia het (x+1)

b) (2x^2-x+2-a) chia het (2x-1)

Answer 1

\(\frac{x^4+x^3+6x^2+5x+5}{x^2+x+1}=\frac{x^4+x^3+x^2+5x^2+5x+5}{x^2+x+1}=\frac{x^2\left(x^2+x+1\right)+5\left(x^2+x+1\right)}{\left(x^2+x+1\right)}=\frac{\left(x^2+x+1\right)\left(x^2+5\right)}{x^2+x+1}=x^2+5\)

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