Đáp án+Giải thích các bước giải:
$$a)A(x)=-x^{4} + 4x^3 - \frac{1}{2}x^2 + x - 3 - 2x^4+ x^3 - \frac{1}{2}x^2 + 2\\ =(-x^{4} - 2x^4)+( 4x^3+ x^3) +\left(- \dfrac{1}{2}x^2- \dfrac{1}{2}x^2\right) + x + (2- 3 )\\ =-3x^4+5x^3 -x^2 + x -1\\ B(x)=x^4- x^3 - 3x^2 + 2x - 4 + x^4 - 4x^3 + x^2 - 3x\\ =(x^4+ x^4)+(- x^3- 4x^3) + (x^2 - 3x^2 )+ (2x - 3x)- 4 \\ =2x^4-5x^3 -2x^2-x- 4 \\ b) A(1)\\ =-3.1^4+5.1^3 -1^2 + 1 -1\\ =-3+5 -1 + 1 -1\\ =1\\ B(-2)\\ =2.(-2)^4-5.(-2)^3 -2.(-2)^2-(-2)- 4 \\ =2.16-5.(-8) -2.4+2- 4 \\ =32+40-8+2- 4 \\ =62\\ c) C(x)= A(x)+B(x)\\ =-3x^4+5x^3 -x^2 + x -1+2x^4-5x^3 -2x^2-x- 4 \\ =(-3x^4+2x^4)+(5x^3-5x^3)+( -x^2-2x^2) +( x -x)+( -1- 4 )\\ =-x^4-3x^2 -5.$$