Question

[Trần Bỏa Trân]

Bài 1: Tìm a sao cho
1. 2𝑥²− 5x + a chia hết cho 2x + 1
2. 𝑥⁴− 9𝑥³+ 21x²+ 𝑥 + 𝑎 chia hết cho x² − 𝑥 − 2

Answer 1

[Lấp La Lấp Lánh]

1) \(2x^2-5x+a=x\left(2x+1\right)-3\left(2x+1\right)+3+a=\left(2x+1\right)\left(x-3\right)+3+a⋮\left(2x+1\right)\)

\(\Rightarrow3+a=0\Rightarrow a=-3\)

2) \(x^4-9x^3+21x^2+x+a=x^2\left(x^2-x-2\right)-8x\left(x^2-x-2\right)+15\left(x^2-x-2\right)+30+a=\left(x^2-x-2\right)\left(x^2-8x+15\right)+30+a⋮\left(x^2-x-2\right)\)

\(\Rightarrow30+a=0\Rightarrow a=-30\)