Question

1/ phân tích đa thức thành nhân tử:

a) 7x-6x²-2

b) 2x²+3x-5

c) 16x-5x²-3

2/ Cho a+b+c=0. Chứng minh a³+b³+c³⁼3ab

Answer 1

1, 

\(a,7x-6x^2-2=-6x^2+7x-2=-6x^2+3x+4x-2\)

\(=-3x\left(2x-1\right)+2\left(2x-1\right)=\left(2x-1\right)\left(2-3x\right)\)

\(b,2x^2+3x-5=2x^2-2x+5x-5\)

\(=2x\left(x-1\right)+5\left(x-1\right)=\left(x-1\right)\left(2x+5\right)\)

\(c,16x-5x^2-3=-5x^2+x+15x-3\)

\(=-x\left(5x-1\right)+3\left(5x-1\right)=\left(5x-1\right)\left(3-x\right)\)

2,

\(a+b+c=0=>a+b=-c=>\left(a+b\right)^3=\left(-c\right)^3\)

\(=>a^3+b^3+3a^2b+3ab^2=-c^3\)

\(=>a^3+b^3+c^3=-3ab\left(a+b\right)\)

\(=>a^3+b^3+c^3=-3ab\left(-c\right)=3abc\)(vì a+b=-c)

Answer 2

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

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

\(=2x\left(x-1\right)+5\left(x-1\right)\)

\(=\left(x-1\right)\left(2x+5\right)\)