Question

phân tích đa thức bằng phương pháp tổng hợp:

a.16x-5x²-3

b.x^3-x+3x^2y+3xy^2+y^3-y

c.x^4+8x

d.x^2+x-6

e.5x^2-10xy+5y^2-20z^2

f.2(x^5)-x^2-5x

g.x^3-3x^2-4x+12

h.x^4-5x^2+4

Answer 1

a.16x-5x²-3 = - ( 5x²-16x+3) = -( 5x²-15x-x+3)= -[ 5x(x-3)-(x-3)] = -(5x-1)(x-3) 

b.x^3-x+3x^2y+3xy^2+y^3-y = \(\left(x^3+3x^2y+3xy^2+y^3\right)-\)\(\left(x+y\right)\)

\(=\left(x+y\right)^3-\left(x+y\right)=\)\(\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)

\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)

c.x^4+8x = \(x\left(x^3+8\right)=x\left(x+2\right)\left(x^2-2x+4\right)\)

d.x^2+x-6 = \(x^2+3x-2x-6=x\left(x+3\right)-2\left(x+3\right)\)

\(=\left(x+3\right)\left(x-2\right)\)

e.5x^2-10xy+5y^2-20z^2\(=5\left(x^2-2xy+y^2-4z^2\right)\)

\(=5\left[\left(x-y\right)^2-\left(2z\right)^2\right]\)

\(=5\left(x-y+2z\right)\left(x-y-2z\right)\)

f.2(x^5)-x^2-5x ( mik ko bik làm)

g.x^3-3x^2-4x+12 = \(x^2\left(x-3\right)-4\left(x-3\right)=\left(x^2-2^2\right)\left(x-3\right)\)

\(=\left(x-2\right)\left(x+2\right)\left(x-3\right)\)

h.x^4-5x^2+4 \(=\left(x^2\right)^2-4x^2+4-x^2\)

\(=\left(x^2-2\right)-x^2=\left(x^2-2+x\right)\left(x^2-2-x\right)\)