Phân tích các đa thức sau thành nhân tử:
a) 2x4 - 3x3- 6x2 + 16x
b) 2x3 - 2xy2 - 8x2 + 8x
c) 8xy2 + 8x2y + 2x3 - xz2
d) 4a4 + 10a3 - 15a - 9
e) 4a3 + 2ab - 4a2 - ab2
f) 5a2 - 14a + 8
g) 2ax + 3ay - 2x - 3y
h) x3 + 10xy - 5x2y - 8
i) x3 - xy2 - x + 2x2y
j) 2a2 - 7a + 5
k) 5ab2 - 10abc + 5ac2
l) 2x3 - 2xy2 - 8x2 + 8x
m) a2 - ac + bc - 2ab + b2
n) 2a2 - 11a + 15
o) 2x3 - 2xy2 - 8x2 + 8x
\(A=2x^4+4x^3-7x^3-14x^2+8x^2+16x\)
\(=2x^2\left(x^2+2x\right)-7x\left(x^2+2x\right)+8\left(x^2+2x\right)\)
\(=\left(2x^2-7x+8\right)\left(x^2+2x\right)\)
\(=x\left(x+2\right)\left(2x^2-7x+8\right)\)
\(B=2x\left(x^2-4x+4-y^2\right)\)
\(=2x\left(\left(x-2\right)^2-y^2\right)\)
\(=2x\left(x-y-2\right)\left(x+y-2\right)\)
\(C=x\left(8y^2+8xy+2x^2-z^2\right)\)
\(=x\left(2\left(4y^2+4xy+x^2\right)-z^2\right)\)
\(=x\left(2\left(x+2y\right)^2-z^2\right)\)
\(=x\left(\sqrt{2}x+2\sqrt{2}y-z\right)\left(\sqrt{2}x+2\sqrt{2}y+z\right)\)
\(D=4a^4+10a^3+6a^2-6a^2-15a-9\)
\(=2a^2\left(2a^2+5a+3\right)-3\left(2a^2+5a+3\right)\)
\(=\left(2a^2-3\right)\left(2a^2+5a+3\right)\)
\(E=4a^3-ab^2+2ab-4a^2\)
\(=a\left(4a^2-b^2\right)-2a\left(2a-b\right)\)
\(=a\left(2a+b\right)\left(2a-b\right)-2a\left(2a-b\right)\)
\(=\left(2a-b\right)\left(2a^2+ab-2a\right)\)
\(F=5a^2-10a-4a+8\)
\(=5a\left(a-2\right)-4\left(a-2\right)\)
\(=\left(5a-4\right)\left(a-2\right)\)
\(G=a\left(2x+3y\right)-\left(2x+3y\right)\)
\(=\left(a-1\right)\left(2x+3y\right)\)
\(H=x^3-8+10xy-5x^2y\)
\(=\left(x-2\right)\left(x^2+2x+4\right)-5xy\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+4-5xy\right)\)
\(I=x\left(x^2-y^2-1+2y\right)\)
\(=x\left(x^2-\left(y-1\right)^2\right)\)
\(=x\left(x-y+1\right)\left(x+y-1\right)\)
\(J=2a^2-2a-5a+5\)
\(=2a\left(a-1\right)-5\left(a-1\right)\)
\(=\left(2a-5\right)\left(a-1\right)\)
\(K=5a\left(b^2-2bc+c^2\right)\)
\(=5a\left(b-c\right)^2\)
\(L=2x\left(x^2-y^2-4x+4\right)\)
\(=2x\left(\left(x-2\right)^2-y^2\right)\)
\(=2x\left(x-y-2\right)\left(x+y-2\right)\)
\(M=a^2-2ab+b^2-ac+bc\)
\(=\left(a-b\right)^2-c\left(a-b\right)\)
\(=\left(a-b\right)\left(a-b-c\right)\)
\(N=2a^2-6a-5a+15\)
\(=2a\left(a-3\right)-5\left(a-3\right)\)
\(=\left(2a-5\right)\left(a-3\right)\)
\(O=2x\left(x^2-4x+4-y^2\right)\)
\(=2x\left(\left(x-2\right)^2-y^2\right)\)
\(=2x\left(x-y-2\right)\left(x+y-2\right)\)
