Bài 4
\(A\left(x\right)=\left(x^2-5\right)\left(x+3\right)+\left(x+4\right)\left(x-x^2\right)\)
\(=x^3+3x^2-5x-15+x^2-x^3+4x-4x^2\)
\(=\left(x^3-x^3\right)+\left(3x^2+x^2-4x^2\right)+\left(-5x+4x\right)-15\)
\(=-x-15\)
Tại \(x=-15\Rightarrow A\left(-15\right)=-\left(-15\right)-15=0\)
Bài 5
\(B\left(x\right)=x^2\left(1+2x\right)-\left(2x+1\right)\left(1+x^2\right)\)
\(=x^2+2x^3-2x-2x^3-1-x^2\)
\(=\left(2x^3-2x^3\right)+\left(x^2-x^2\right)-2x-1\)
\(=-2x-1\)
Tại \(x=\dfrac{1}{2}\Rightarrow B\left(\dfrac{1}{2}\right)=-2.\dfrac{1}{2}-1=-2\)
Bài 6
\(C\left(x\right)=\left(x^2-3x-5\right)\left(1+x\right)-\left(x+1\right)\left(x^2-5\right)\)
\(=x^2+x^3-3x-3x^2-5-5x-x^3+5x-x^2+5\)
\(=\left(x^3-x^3\right)+\left(x^2-3x^2-x^2\right)+\left(-3x-5x+5x\right)+\left(-5+5\right)\)
\(=-3x^2-3x\)
Tại \(x=-\dfrac{4}{3}\Rightarrow C\left(-\dfrac{4}{3}\right)=-3.\left(-\dfrac{4}{3}\right)^2-3.\left(-\dfrac{4}{3}\right)\)
\(=-\dfrac{16}{3}+4\)
\(=-\dfrac{4}{3}\)
