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\(S=x^6-8\)
\(S=\left(x^2\right)^3-2^3\)
\(S=\left(x^2-2\right)\left(x^4+2x^2+4\right)\)
⇒ Chọn C
\(a,x^2+9x+20=x^2+4x+5x+20.\)
\(=x\left(x+4\right)+5\left(x+4\right)=\left(x+4\right)\left(x+5\right)\)
\(b,x^4-5x^2+4=x^4-x^2-4x^2+4\)
\(=x^2\left(x^2-1\right)-4\left(x^2-1\right)=\left(x^2-1\right)\left(x^2-4\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\)
\(c,x^4+4=x^4+4x^2+4-4x^2\)
\(=\left(x^2-2\right)-\left(2x\right)^2=\left(x^2-2x-2\right)\left(x^2+2x-2\right)\)
\(d,x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)
\(=x\left(x+3\right)\left(x+1\right)\left(x+2\right)+1\)
\(\left(x^2+3x\right)\left(x^2+3x+2\right)+1\)
\(=\left(x^2+3x\right)\left(x^2+3x\right)+2\left(x^2+3x\right)+1\)
\(=\left(x^2+3x\right)^2+2\left(x^2+3x\right)+1\)
\(=\left(x^2+3x+1\right)^2\)
a) (x-2)(x+2)(x^2-10)-72=(x^2-4)(x^2-82)
b) x^8+x^6+x^4+x^2+1=x^2 (x^4+x^3+x^2+1+1/x^2)
c)(x+y)^4+x^4+y^4=(x+y)^4+(x+y)^4=2 (x+y)^4
a) (x-2)(x+2)(x^2 - 10) -72
= (x^2 - 4)(x^2 - 10) - 72
= x^4 - 4x^2 -10x^2 + 40 - 72
= x^4 - 14x^2 - 32
= x^4 - 16x^2 + 2x^2 - 32
= x^2(x^2 - 16) + 2(x^2 - 16)
= (x^2 - 16)(x^2 + 2)
= (x-4)(x+4)(x^2 + 2)
c) (x+y)4 + x4 + y4
= 2x4 + 4xy3 + 6x2y2 + 4x3y + 2y3
= 2(y4 + 2xy3 + 3x2y2 + 2x3y + x4)
= 2(y2 + xy + y2)2
\(x^8+x^7+1\)
\(=x^8+x^7+x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-xx+1\)
\(=\left(x^8-x^6+x^5-x^3+x^2\right)\)
\(+\left(x^7-x^5+x^4-x^2+x\right)\)
\(+\left(x^6-x^4+x^3-x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
a) x2 - 4x + 3
= x2 - x - 3x + 3
= x(x - 1) - 3(x - 1)
= (x - 1)(x - 3)
b) x2 + 5x + 4
= x2 + x + 4x + 4
= x(x + 1) + 4(x + 1)
= (x + 1)(x + 4)
c) x2 - x - 6
= x2 + 2x - 3x - 6
= x(x + 2) - 3(x + 2)
= (x + 2)(x - 3)
x2 - 4x + 3
= x2 - x - 3x + 3
= (x2 - x) - (3x - 3)
= x(x - 1) - 3(x - 1)
= (x - 3) (x - 1)
\(P=x^2\left(x^2-4\right)=x^2\left(x-2\right)\left(x+2\right)\\ =>A\)