a) Ta có: \(P\left(x\right)=5x^2+3x^3-5x^2+2x^3-2+4x-4x^2+x^3\)

\(=\left(3x^3+2x^3+x^3\right)+\left(5x^2-5x^2-4x^2\right)+4x-2\)

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

Ta có: \(Q\left(x\right)=6x-x^3+5-6x^3-6+7x^2-10x^2\)

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

\(=-7x^3-3x^2+6x-1\)

b) Ta có: P(x)+Q(x)

\(=6x^3-4x^2+4x-2-7x^3-3x^2+6x-1\)

\(=-x^3-7x^2+10x-3\)

Ta có: P(x)-Q(x)

\(=6x^3-4x^2+4x-2+7x^3+3x^2-6x+1\)

\(=13x^3-x^2-2x-1\)

`@` `\text {Ans}`

`\downarrow`

`a)`

`3x(4x-1) - 2x(6x-3) = 30`

`=> 12x^2 - 3x - 12x^2 + 6x = 30`

`=> 3x = 30`

`=> x = 30 \div 3`

`=> x=10`

Vậy, `x=10`

`b)`

`2x(3-2x) + 2x(2x-1) = 15`

`=> 6x- 4x^2 + 4x^2 - 2x = 15`

`=> 4x = 15`

`=> x = 15/4`

Vậy, `x=15/4`

`c)`

`(5x-2)(4x-1) + (10x+3)(2x-1) = 1`

`=> 5x(4x-1) - 2(4x-1) + 10x(2x-1) + 3(2x-1)=1`

`=> 20x^2-5x - 8x + 2 + 20x^2 - 10x +6x - 3 =1`

`=> 40x^2 -17x - 1 = 1`

`d)`

`(x+2)(x+2)-(x-3)(x+1)=9`

`=> x^2 + 2x + 2x + 4 - x^2 - x + 3x + 3=9`

`=> 6x + 7 =9`

`=> 6x = 2`

`=> x=2/6 =1/3`

Vậy, `x=1/3`

`e)`

`(4x+1)(6x-3) = 7 + (3x-2)(8x+9)`

`=> 24x^2 - 12x + 6x - 3 = 7 + (3x-2)(8x+9)`

`=> 24x^2 - 12x + 6x - 3 = 7 + 24x^2 +11x - 18`

`=> 24x^2 - 6x - 3 = 24x^2 + 18x -11`

`=> 24x^2 - 6x - 3 - 24x^2 + 18x + 11 = 0`

`=> 12x +8 = 0`

`=> 12x = -8`

`=> x= -8/12 = -2/3`

Vậy, `x=-2/3`

`g)`

`(10x+2)(4x- 1)- (8x -3)(5x+2) =14`

`=> 40x^2 - 10x + 8x - 2 - 40x^2 - 16x + 15x + 6 = 14`

`=> -3x + 4 =14`

`=> -3x = 10`

`=> x= - 10/3`

Vậy, `x=-10/3`

Hello các bạn còn đó ko?

Câu a : \(4x^3-5x^2+6x+9\)

\(=4x^3+3x^2-8x^2-6x+12x+9\)

\(=\left(4x^3+3x^2\right)-\left(8x^2+6x\right)+\left(12x+9\right)\)

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

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

Câu b : \(5x^3-12x^2+14x-4\)

\(=5x^3-10x^2-2x^2+10x+4x-4\)

\(=\left(5x^3-2x^2\right)-\left(10x^2-4x\right)+\left(10x-4\right)\)

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

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

Câu c : \(x^3-5x^2+2x+8\)

\(=x^3+x^2-6x^2-6x+8x+8\)

\(=\left(x^3+x^2\right)-\left(6x^2+6x\right)+\left(8x+8\right)\)

\(=x^2\left(x+1\right)-6x\left(x+1\right)+8\left(x+1\right)\)

\(=\left(x+1\right)\left(x^2-6x+8\right)\)

\(=\left(x+1\right)\left[x^2-2x-4x+8\right]\)

\(=\left(x+1\right)\left[x\left(x-2\right)-4\left(x-2\right)\right]\)

\(=\left(x+1\right)\left(x-2\right)\left(x-4\right)\)

Câu d : \(4x^3+5x^2+10x-12\)

\(=4x^3+8x^2-3x^2+16x-6x-12\)

\(=\left(4x^3-3x^2\right)+\left(8x^2-6x\right)+\left(16x-12\right)\)

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

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

b. 6x(x - 5) - x(6x + 3)

= x(6x - 30) - x(6x + 3)

= x(6x - 30 - 6x - 3)

= x(-33)

= -33x