Question

Phân tích các đa thức sau thành nhân tử

a) 2x + 10y

b) x\(^2\) + xy + x

c) 3x\(^2\)y - 6xy + 12xy\(^2\)

d) y. (x - 2) - 2x. (x - 2)

e) x\(^2\) - 2x - 15

f) x. (y - x) - 2y. (y - x)

g) 2x\(^2\). (x - 2y) + xy. (x - 2y)

Answer 1

a: \(2x+10y=2\cdot x+2\cdot5y=2\left(x+5y\right)\)

b: \(x^2+xy+x=x\cdot x+x\cdot y+x\cdot1=x\left(x+y+1\right)\)

c: \(3x^2y-6xy+12xy^2\)

\(=3xy\cdot x-3xy\cdot2+3xy\cdot4y\)

\(=3xy\left(x-2+4y\right)\)

d: \(y\left(x-2\right)-2x\left(x-2\right)\)

\(=\left(x-2\right)\left(y-2x\right)\)

e: \(x^2-2x-15\)

\(=x^2-5x+3x-15\)

\(=x\left(x-5\right)+3\left(x-5\right)\)

\(=\left(x-5\right)\left(x+3\right)\)

f: \(x\left(y-x\right)-2y\left(y-x\right)\)

\(=\left(y-x\right)\left(x-2y\right)\)

g: \(2x^2\cdot\left(x-2y\right)+xy\left(x-2y\right)\)

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

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

Answer 2

\(a)2x+10y=2(x+5y) \)

\(b)x^2+xy+x=x(x+y+1) \)

\(c)3x^2y-6xy+12xy^2=3xy(x-2+4y)\)

\(d)y(x-2)-2x(x-2)=(y-2x)(x-2)\)

\(e)\)\(x^2-2x-15\\= x^2-5x+3x-15\\ =x\left(x-3\right)+5\left(x-3\right)\\ =\left(x+5\right)\left(x-3\right)\)

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