\(g\left(x\right)=x^2+x-2=x^2+2x-x-2\)
=> \(g\left(x\right)=x\left(x+2\right)-\left(x+2\right)=\left(x-1\right)\left(x+2\right)\)
Gọi thương của pháp chia là Q(x)
=> \(f\left(x\right)=g\left(x\right).Q\left(x\right)\)
=> \(x^3-2x^2-5x+10+2a=\left(x+2\right)\left(x-1\right).Q\left(x\right)\)
- Thay x = -2
=> \(\left(-2\right)^3-2.\left(-2\right)^2-5.\left(-2\right)+10+2a=\left(-2+2\right)\left(-2-1\right).Q\left(x\right)\)
=> \(4+2a=0\)
=> \(2a=-4\)
=> \(a=-2\)
- Thay x = 1
=> \(1^3-2.1^2-5.2+10+2a=\left(1+2\right)\left(1-1\right).Q\left(x\right)\)
=> \(1+2a=0\)
=> \(2a=-1\)
=> \(a=-0,5\)
KL: \(a\in\left\{-2;-0,5\right\}\)