Question

Xác định a,b,c

1) X^3+3x^2-x-3=(x-2)(x^2+bx+c)+a

2) 4x^3+7x-6=(ax+b)(x^2+x+1)+c

Answer 1

1: \(x^3+3x^2-x-3=\left(x-2\right)\left(x^2+bx+c\right)+a\)

\(\Leftrightarrow x^3-2x^2+5x^2-10x+11x-22+19=\left(x-2\right)\left(x^2+bx+c\right)+a\)

\(\Leftrightarrow\left(x-2\right)\left(x^2+5x+11\right)+19=\left(x-2\right)\left(x^2+bx+c\right)+a\)

=>b=5; c=11; c=19

2: \(4x^3+7x-6=\left(ax+b\right)\left(x^2+x+1\right)+c\)

\(\Leftrightarrow4x^3+4x^2+4x-4x^2-4x-4+7x-2=\left(ax+b\right)\left(x^2+x+1\right)+c\)

\(\Leftrightarrow\left(x^2+x+1\right)\left(4x-4\right)+7x-2=\left(ax+b\right)\left(x^2+x+1\right)+c\)

=>a=4; b=-4; c=7x-2