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\(\left(x^2+22x+120\right)\left(x^2+33x+270\right)-2x^2\)
\(=\left(x+10\right)\left(x+12\right)\left(x+18\right)\left(x+15\right)-2x^2\)
\(=\left(x^2+28x+180\right)\left(x^2+27x+280\right)-2x^2\)
\(=\left(x^2+180\right)^2+55x\left(x^2+180\right)+754x^2\)
\(=\left(x^2+29x+180\right)\left(x^2+26x+180\right)\)
\(=\left(x+9\right)\left(x+20\right)\left(x^2+26x+180\right)\)
a: \(=\dfrac{6x^2+9x+8x+12}{2x+3}=\dfrac{3x\left(2x+3\right)+4\left(2x+3\right)}{2x+3}\)
=3x+4
b: \(=\dfrac{5x^2-2x+15x-6}{5x-2}\)
\(=\dfrac{x\left(5x-2\right)+3\left(5x-2\right)}{5x-2}=x+3\)
c: \(=\dfrac{-8x^2+20x+2x-5-10}{2x-5}=-4x+1+\dfrac{-10}{2x-5}\)
d: \(=\dfrac{14x^2-35x+2x-5}{2x-5}=\dfrac{7x\left(2x-5\right)+\left(2x-5\right)}{2x-5}\)
=7x+1
e: \(=\dfrac{2x^3+x^2+6x^2+3x+12x+6}{2x+1}\)
\(=\dfrac{x^2\left(2x+1\right)+3x\left(2x+1\right)+6\left(2x+1\right)}{2x+1}=x^2+3x+6\)
f: \(=\dfrac{x^3-2x^2+6x^2-12x+x-2}{x-2}=x^2+6x+1\)
g: \(=\dfrac{12x^3+6x^2-4x^2-2x+6x+3}{2x+1}=6x^2-2x+3\)
b) 3x4-3x3+9x3-9x2-24x2+24x-48x+48
=3x3(x-1)+9x2(x-1)-24x(x-1)-48(x-1)
=(x-1)(3x3+9x2-24x-48)
=3(x-1)(x3+3x2-8x-16)
\(x^3+x^2+9x-10x^2-10x+25x+25\)
\(=x^2\left(x+1\right)-10x\left(x+1\right)+25\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-10x+25\right)=\left(x+1\right)\left(x-5\right)^2\)
\(2x^4+x^3-22x^2+15x-36\)
\(=\left(2x^4-6x^3\right)+\left(7x^3-21x^2\right)+\left(-x^2+3x\right)+\left(12x-36\right)\)
\(=\left(x-3\right)\left(2x^3+7x^2-x+12\right)\)
\(=\left(x-3\right)\left(\left(2x^3+8x^2\right)+\left(-x^2-4x\right)+\left(3x+12\right)\right)\)
\(=\left(x-3\right)\left(x+4\right)\left(2x^2-x+3\right)\)
a) \(x^3+6x^2+3x-10\)
\(=x^3-x^2+7x^2-7x+10x-10\)
\(=x^2\left(x-1\right)+7x\left(x-1\right)+10\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+7x+10\right)\)
\(=\left(x-1\right)\left(x^2+2x+5x+10\right)\)
\(=\left(x-1\right)\left(x+2\right)\left(x+5\right)\)
b) \(x^3+3x^2-33x-35\)
\(=x^3-5x^2+8x^2-40x+7x-35\)
\(=x^2\left(x-5\right)+8x\left(x-5\right)+7\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2+8x+7\right)\)
\(=\left(x-5\right)\left(x^2+x+7x+7\right)\)
\(=\left(x-5\right)\left(x+1\right)\left(x+7\right)\)
xin lỗi nhé mình mới có lớp 6 à nên ko bít
tha lỗi cho mình nhé!
\(\left(x^2+22x-120\right)\left(x^2+33x+270\right)-2x^2\)
\(=x^4+55x^3+876x^2+1980x-32400-2x^2\)
\(=x^4+55x^3+874x^2+1980x-32400\)