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\(3x^4-48\)
\(=\left(3x^4-6x^3\right)+\left(6x^3-12x^2\right)+\left(12x^2-24x\right)+\left(24x-48\right)\)
\(=3x^3\left(x-2\right)+6x^2\left(x-2\right)+12x\left(x-2\right)+24\left(x-2\right)\)
\(=\left(x-2\right)\left[\left(3x^3+6x^2\right)+\left(12x+24\right)\right]\)
\(=\left(x-2\right)\left[3x^2\left(x+2\right)+12\left(x+2\right)\right]\)
\(=\left(x-2\right)\left(x+2\right)\left(3x^2+12\right)\)
\(x^4-8x\)
\(=x\left(x^3-8\right)\)
\(=x\left[\left(x^3-2x^2\right)+\left(2x^2-4x\right)+\left(4x-8\right)\right]\)
\(=x\left[x^2\left(x-2\right)+2x\left(x-2\right)+4\left(x-2\right)\right]\)
\(=x\left(x-2\right)\left(x^2+2x+4\right)\)
x^3 + 3x -4 = x^3 - 1 + 3x - 3 = (x-1)(x^2-x+1) + 3(x-1) = (x-1)(x^2-x+1+3) = (x-1)(x^2-x+4)
nhớ cho mik nha
x2 + 14x + 48 = x2 + 6x + 8x + 48
= ( x2 + 6x ) + ( 8x + 48 )
= x . ( x + 6 ) + 8 . ( x + 6 )
= ( x + 6 ) . ( x + 8 )
\(1-3x-x^3+3x^2\)\(=\left(1-x^3\right)+\left(3x^2-3x\right)\)
\(=\left(1-x\right)\left(x^2+x+1\right)+3x\left(x-1\right)\)
\(=\left(x-1\right)\left(3x-x^2-x-1\right)=\left(x-1\right)\left(2x-x^2-1\right)\)
\(x^8+3x^4+1=\left(x^8+\frac{2.3x^4}{2}+\frac{9}{4}\right)-\frac{5}{4}\)
\(=\left(x^4+\frac{3}{2}\right)^2-\frac{5}{4}=\left(x^4+\frac{3-\sqrt{5}}{2}\right)\left(x^4+\frac{3+\sqrt{5}}{2}\right)\)
\(3x^4-48=3\left(x^4-16\right)=3\left[\left(x^2\right)^2-4^2\right]\\ =3\left(x^2-4\right)\left(x^2+4\right)\\ =3\left(x-2\right)\left(x+2\right)\left(x^2+4\right)\)
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