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

\(=10x^4-15x^3-4x^3+6x^2+2x^2-3x\)

\(=10x^4-19x^3+8x^2-3x\)

b) \(\left(18x^4y^3-6x^2y^3+12x^3y^4z\right)\)

\(=6x^2y^3\left(3x^2-1+2xyz\right)\)

\(\Rightarrow\left(18x^4y^3-6x^2y^3+12x^3y^4z\right):6x^2y^3\)

\(=\left[6x^2y^3\left(3x^2-1+2xyz\right)\right]:6x^2y^3\)

\(=3x^2+2xyz-1\)

c) \(\left(6x^3-7x^2-x+1\right)\)

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

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

\(\Rightarrow\left(6x^3-7x^2-x+1\right):\left(2x+1\right)\)

\(=\left[\left(2x+1\right)\left(3x^2-5x+1\right)-1\right]:\left(2x+1\right)\)

\(=3x^2-5x+1\) (Dư \(-1\))

a)(5x²-2x+1).(2x²-3x)

=10x⁴-4x³+2x²-15x³+6x²-3x

=10x⁴-19x³+8x²-3x

b)(18x⁴y³-6x²y³+12x³y⁴z):6x²y³

=(18x⁴y³:6x²y³)-(6x²y³:6x²y³)+(12x³y⁴z:6x²y³)

=3x²y-xy+2xyz

\(=12x^3-10x+18x^2-15\)

\(\left(6x^3-7x^2-x+2\right):\left(2x+1\right)\\ =\left[\left(6x^3-6x^2\right)-\left(x^2-x\right)-\left(2x-2\right)\right]:\left(2x+1\right)\\ =\left[\left(x-1\right)\left(6x^2-x-2\right)\right]:\left(2x+1\right)\\ =\left\{\left(x-1\right)\left[\left(6x^2+3x\right)-\left(4x+2\right)\right]\right\}:\left(2x+1\right)\\ =\left[\left(x-1\right)\left(3x-2\right)\left(2x+1\right)\right]:\left(2x+1\right)\\ =\left(x-1\right)\left(3x-2\right)\)

\(\left(6x^2-5\right)\left(2x+3\right)=2x\left(6x^2-5\right)+3\left(6x^2-5\right)=12x^3-10x+18x^2-15\)

\(a,=\left(6x^3+3x^2-10x^2-5x+4x+2\right):\left(2x+1\right)\\ =\left(2x+1\right)\left(3x^2-5x+2\right):\left(2x+1\right)=3x^2-5x+2\\ b,=\left(x^4-2x^3+3x^2+x^3-2x^2+3x\right):\left(x^2-2x+3\right)\\ =\left(x^2-2x+3\right)\left(x^2+x\right):\left(x^2-2x+3\right)=x^2+x\)

A(x)=(7x²-5x²-2x²)-(6x³-10x³)+2x-12

A(x)=-4x³+2x-12

Sắp xếp:-4x³+2x-12

\(A\left(x\right)=\left(7x^2-5x^2-2x^2\right)-\left(6x^3-10x^3\right)+2x-12\)

\(A\left(x\right)=-4x^3+2x-12\)

Sắp xếp:\(-4x^3+2x-12\)

\(=\left(6x^3+3x^2-10x^2-5x+4x+2\right):\left(2x+1\right)\\ =\left[3x^2\left(2x+1\right)-5x\left(2x+1\right)+2\left(2x+1\right)\right]:\left(2x+1\right)\\ =3x^2-5x+2\)

\(=3x^2-\dfrac{7}{2}x-2+x+6x^3-7x^2+x+2\\ =-4x^2-\dfrac{7}{2}x+6x^3\)

Để 6 x 3   –   7 x 2  – x + a chia 2x + 1 dư 2 thì a – 2 = 2 ó a = 4

Đáp án cần chọn là: D

1: Sửa đề: 3x-5

\(=\dfrac{-x^2\left(3x-5\right)-3\left(3x-5\right)}{3x-5}=-x^2-3\)

2: \(=\dfrac{5x^4-5x^3+14x^3-14x^2+12x^2-12x+8x-8}{x-1}\)

=5x^2+14x^2+12x+8

3: \(=\dfrac{5x^3+10x^2+4x^2+8x+4x+8}{x+2}=5x^2+4x+4\)

4: \(=\dfrac{\left(x^2-1\right)\left(x^2+1\right)-2x\left(x^2-1\right)}{x^2-1}=x^2+1-2x\)

5: \(=\dfrac{x^2\left(5-3x\right)+3\left(5-3x\right)}{5-3x}=x^2+3\)

=12x4-14x3-2x2+4x+6x3-7x2-x+2

=12x4-8x3-9x2+3x+2

\(=\dfrac{6x^3+3x^2-10x^2-5x+4x+2}{2x+1}=3x^2-5x+2\)

=3x²-5x+2