\(a,3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)

\(=3x^2-6x-5x+5x^2-8x^2+24\)

\(=\left(3x^2+5x^2-8x^2\right)+\left(-6x-5x\right)+24\)

\(=0-11x+24\)

\(=-11x+24\)

\(b,\left(7x-3\right)\left(2x+1\right)-\left(5x-2\right)\left(x+4\right)-9x^2+17x\)

\(=14x^2+7x-6x-3-5x^2-20x+2x+8-9x^2+17x\)

\(=\left(14x^2-5x^2-9x^2\right)+\left(7x-6x-20x+2x+17x\right)+\left(-3+8\right)\)

\(=0+0+5\)

\(=5\)

7x-2x=6 mũ 2 +44:11

5x=36+4

5x=40

x=40:5=8

4x³ - 13x² + 9x - 18

= 4x³ - 12x² - x² + 3x + 6x - 18

= 4x²(x - 3) - x(x - 3) + 6(x - 3)

= (x - 3)(4x² - x + 6)

x² + 5x - 6

= x² + 2x + 3x - 6

= x(x + 2) - 3(x + 2)

= (x + 2)(x - 3)

x³ + 8x² + 17x + 10

= x³ + x² + 7x² + 7x + 10x + 10

= x²(x + 1) + 7x(x + 1) + 10(x + 1)

= (x + 1)(x² + 7x + 10)

= (x + 1)(x² + 5x + 2x + 10)

= (x + 1)[ x(x + 5) + 2(x + 5)]

= (x + 1)(x + 5)(x + 2)

x³ + 3x² + 6x + 4

= x³ + 3x² + 3x + 1 + 3x + 3

= (x + 1)³ + 3(x + 1)

= (x + 1)[(x + 1)² + 3]

= (x + 1)(x² + 2x + 1 + 3)

= (x + 1)(x² + 2x + 4)

2x³ - 12x² + 17x - 2

= 2x³ - 8x² - 4x² + x + 16x - 2

= (2x³ - 8x² + x) - (4x² - 16x + 2)

= x(2x² - 8x + 1) - 2(2x² - 8x + 1)

= (2x² - 8x + 1)(x - 2)

a)⇔ x-2x-2-17x-4x+24>0

⇔22-22x>0

⇔22(1-x)>0

⇔\(\left[{}\begin{matrix}22>0\\1-x>0\end{matrix}\right.\left[{}\begin{matrix}22>0\\x>1\end{matrix}\right.\)

b) ⇔ 12x+1≥4(9x+3)-3(8x+1)

⇔12x+1≥36x+12-24x-3

hết bt làm r xin lỗi nha

một đòn bẫy dài một mét .đặt ở đâu để có thể dùng 3600n có thể nâng tảng đá nặng 120kg?

a)

\(\dfrac{x^3+x^2-4x-4}{x^3+8x^2+17x+10}\)

\(=\dfrac{x^2\left(x+1\right)-4\left(x+1\right)}{x^3+2x^2+6x^2+12x+5x+10}\)

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

\(=\dfrac{\left(x+1\right)\left(x-2\right)\left(x+2\right)}{\left(x+2\right)\left(x^2+6x+5\right)}\)

\(=\dfrac{\left(x+1\right)\left(x-2\right)\left(x+2\right)}{\left(x+2\right)\left[x\left(x+5\right)+\left(x+5\right)\right]}\)

\(=\dfrac{\left(x+1\right)\left(x-2\right)\left(x+2\right)}{\left(x+2\right)\left(x+5\right)\left(x+1\right)}\)

\(=\dfrac{x-2}{x+5}\)

b)

\(\dfrac{x^4+6x^3+9x^2-1}{x^4+6x^3+7x^2-6x+1}\)

\(=\dfrac{x^4+3x^3+x^2+3x^3+9x^2+3x-x^2-3x-1}{x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1}\)

\(=\dfrac{x^2\left(x^2+3x+1\right)+3x\left(x^2+3x+1\right)-\left(x^2+3x+1\right)}{x^2\left(x^2+3x-1\right)+3x\left(x^2+3x-1\right)-\left(x^2+3x-1\right)}\)

\(=\dfrac{\left(x^2+3x+1\right)\left(x^2+3x-1\right)}{\left(x^2+3x-1\right)\left(x^2+3x-1\right)}\)

\(=\dfrac{x^2+3x+1}{x^2+3x-1}\)

a) \(x^2-9x+14\)

\(=x^2-2x-7x+14\)

\(=x\left(x-2\right)-7\left(x-2\right)\)

\(=\left(x-2\right)\left(x-7\right)\)

b) \(x^2+17x-18\)

\(=x^2+18x-x-18\)

\(=x\left(x+18\right)-\left(x+18\right)\)

\(=\left(x+18\right)\left(x-1\right)\)

c) \(2x^2-7x+3\)

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

\(=x\left(2x-1\right)-3\left(2x-1\right)\)

\(=\left(2x-1\right)\left(x-3\right)\)

d) \(x^2-25x+144\)

\(=x^2-9x-16x+144\)

\(=x\left(x-9\right)-15\left(x-9\right)\)

\(=\left(x-9\right)\left(x-15\right)\)