Question

Đặt nhân tử :
a) 10x² -29x+10

b) x²-4xy+3y²

c) 8-x³

d) 2x² -11x+12

e) -2x² +5x-3

f) x²-9x+20

h) 2a²-7a+3

i) a²-a-6

k) x²+x-12

m) 3(x+1)²-4x²-4x

n) 3x(1-2x) -10x+5

o) x² +xy-xz-yz

Answer 1

a) \(10x^2-29x+10\)

\(=10x^2-4x-25x+10\)

\(=2x\left(5x-2\right)-5\left(5x-2\right)\)

\(=\left(5x-2\right)\left(2x-5\right)\)

Answer 2

Answer 3

\(\text{a) }10x^2-29x+10\\ =10x^2-25-4x+10\\ =5x\left(2x-5\right)-2\left(2x-5\right)\\ =\left(5x-2\right)\left(2x-5\right)\)

\(\text{b) }x^2-4xy+3y^2\\ =x^2-3xy-xy+3y^2\\ =x\left(x-3y\right)-y\left(x-3y\right)\\ =\left(x-y\right)\left(x-3y\right)\)

\(\text{c) }8-x^3=\left(2-x\right)\left(4+2x+x^2\right)\)

\(\text{d) }2x^2-11x+12\\ =2x^2-8x-3x+12\\ =2x\left(x-4\right)-3\left(x-4\right)\\ =\left(2x-3\right)\left(x-4\right)\)

\(\text{e) }-2x^2+5x-3\\ =-2x^2+2x+3x-3\\ =\left(2x-2x^2\right)-\left(3-3x\right)\\ =2x\left(1-x\right)-3\left(1-x\right)\\ =\left(2x-3\right)\left(1-x\right)\)

\(\text{f) }x^2-9x+20\\ =x^2-4x-5x+20\\ =x\left(x-4\right)-5\left(x-4\right)\\ =\left(x-5\right)\left(x-4\right)\)

\(\text{h) }2a^2-7a+3\\ =2a^2-a-6a+3\\ =a\left(2a-1\right)-3\left(2a-1\right)\\ =\left(a-3\right)\left(2a-1\right)\)

\(\text{i) }a^2-a-6\\ =a^2-3a+2a-6\\ =a\left(a-3\right)+2\left(a-3\right)\\ =\left(a+2\right)\left(a-3\right)\)\(\text{k) }x^2+x-12\\ =x^2+4x-3x-12\\ =x\left(x+4\right)-3\left(x+4\right)\\ =\left(x-3\right)\left(x+4\right)\)\(\text{ m) }3\left(x+1\right)^2-4x^2-4x\\ =3\left(x+1\right)^2-\left(4x^2+4x\right)\\ =3\left(x+1\right)^2-4x\left(x+1\right)\\ =\left(3x+3-4x\right)\left(x+1\right)\\ =\left(3-x\right)\left(x+1\right)\) \(\text{n) }3x\left(1-2x\right)-10x+5\\ =3x\left(1-2x\right)+\left(5-10x\right)\\ =3x\left(1-2x\right)+5\left(1-2x\right)\\ =\left(3x+5\right)\left(1-2x\right)\)

\(\text{o) }x^2+xy-xz-yz\\ =x\left(x+y\right)-z\left(x+y\right)\\ =\left(x-z\right)\left(x+y\right)\)