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\(a,\left(x-1\right)^2-2^2=\left(x-1-2\right)\left(x-1+2\right)=\left(x-3\right)\left(x+1\right)\\ b,=\left(2x\right)^2+2.2x.3+3^2\\ =\left(2x+3\right)^2\\ c,=x^3-\left(2y\right)^3\\ =\left(x-2y\right)\left(x^2+2xy+4y^2\right)\\ d,=x^3\left(x^2-1\right)-\left(x^2-1\right)\\ =\left(x^3-1\right)\left(x^2-1\right)\\ =\left(x-1\right)\left(x^2+x+1\right)\left(x-1\right)\left(x+1\right)\\ =\left(x-1\right)\left(x+1\right)\left(x^2+x+1\right)\)
\(e,=-4x^2\left(x-1\right)+\left(x-1\right)\\ =\left(1-4x^2\right)\left(x-1\right)\\ =\left(1-2x\right)\left(1+2x\right)\left(x-1\right)\)
\(f,=\left(2x\right)^3+3.\left(2x\right)^2.1+3.2x.1^2+1^3\\ =\left(2x+1\right)^3\)
Các biểu thức không phải đa thức bậc 4 là:
\(x^4-\dfrac{1}{3}x^3y^2\)
\(B=\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
\(\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}-\dfrac{1}{2}\right)\left(x^2+x+\dfrac{3}{2}+\dfrac{1}{2}\right)-12\)
\(\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}\right)^2-\dfrac{1}{4}-12\)
\(\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}\right)^2-\dfrac{49}{4}\)
\(\Leftrightarrow B=\left(x^2+x+\dfrac{3}{2}-\dfrac{7}{2}\right)\left(x^2+x+\dfrac{3}{2}+\dfrac{7}{2}\right)\)
\(\Leftrightarrow B=\left(x^2+x-2\right)\left(x^2+x+5\right)\)
\(C=x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)
\(\Leftrightarrow C=x\left(x+3\right)\left(x+1\right)\left(x+2\right)+1\)
\(\Leftrightarrow C=\left(x^2+3x\right)\left(x^2+x+2x+2\right)+1\)
\(\Leftrightarrow C=\left(x^2+3x\right)\left(x^2+3x+2\right)+1\)
\(\Leftrightarrow C=\left(x^2+3x+1-1\right)\left(x^2+3x+1+1\right)+1\)
\(\Leftrightarrow C=\left(x^2+3x+1\right)^2-1+1\)
\(\Leftrightarrow C=\left(x^2+3x+1\right)^2\)
\(D=\left(x-1\right)\left(x-3\right)\left(x-5\right)\left(x-7\right)-20\)
\(\Leftrightarrow D=\left(x-1\right)\left(x-7\right)\left(x-3\right)\left(x-5\right)-20\)
\(\Leftrightarrow D=\left(x^2-x-7x+7\right)\left(x^2-3x-5x+15\right)-20\)
\(\Leftrightarrow D=\left(x^2-8x+7\right)\left(x^2-8x+15\right)-20\)
\(\Leftrightarrow D=\left(x^2-8x+11-4\right)\left(x^2-8x+11+4\right)-20\)
\(\Leftrightarrow D=\left(x^2-8x+11\right)^2-16-20\)
\(\Leftrightarrow D=\left(x^2-8x+11\right)^2-36\)
\(\Leftrightarrow D=\left(x^2-8x+11-6\right)\left(x^2-8x+11+6\right)\)
\(\Leftrightarrow D=\left(x^2-8x+5\right)\left(x^2-8x+17\right)\)
:D
a, ( x2 + x )2 - 14 ( x2 + x ) + 24
= (x2 + x)2 - 2(x2 + x) -12(x2 + x) + 24
= (x2 + x).(x2 + x -2) - 12(x2 + x -2)
= (x2 + x -2).(x2 + x -12)
= (x2 + 2x - x - 2).(x2 + 4x - 3x - 12)
=[x.(x+2)-(x+2)].[x.(x+4)-3(x+4)]
= (x+2).(x-1).(x+4).(x-3)
= x4 + 2x3 - 13x2 - 14x + 24
b, ( x2 + x )2 + 4x2 + 4x - 12
= x4 + 2x3 + x2 + 4x2 + 4x -12
= x4 + 2x3 + 5x2 + 4x -12
c, x4 + 2x3 + 5x2 + 4x - 12
= x4 - x3 + 3x3 - 3x2 + 8x2 - 8x +12x -12
= x3(x-1) + 3x2(x-1) + 8x(x-1) + 12(x-1)
= (x-1) . (x3 + 3x2 + 8x +12)
= (x-1) . ( x3 +2x2 + x2 + 2x + 6x +12)
= (x-1). [x2(x+2) + x(x+2) + 6(x+2)]
= (x-1).(x+2).(x2 + x+ 6)
Đáp án cần chọn là: A