[tex]W(x)=(2x+b)(x^2+3x+1)=2x^3+6x^2+2x+bx^2+3bx+b\\\\F(x)=(ax+3)(x+1)^2=(ax+3)(x^2+2x+1)=ax^3+2ax^2+ax+3x^2+6x+3\\\\H(x)=x^3+6x^2+10x+2[/tex]
[tex]W(x)-F(x)=2x^3+6x^2+2x+bx^2+3bx+b-(ax^3+2ax^2+ax+3x^2+6x+3)=\\\\2x^3+6x^2+2x+bx^2+3bx+b-ax^3-2ax^2-ax-3x^2-6x-3=\\\\- ax^3 + 2x^3 - 2ax^2 + bx^2 + 3x^2 - ax + 3bx - 4x + b - 3=\\\\(2 - a)x^3 - (2a - b - 3)x^2 - (a - 3b + 4)x + b - 3[/tex]
[tex](2 - a)x^3 - (2a - b - 3)x^2 - (a - 3b + 4)x + b - 3=x^3+6x^2+10x+2[/tex]
Porównujemy współczynniki
[tex]2-a=1\\a=2-1\\a=1\\\\\\b-3=2\\b=2+3\\b=5[/tex]
a=1, b=5
