Question

1) phân tích da thức thành nhân tử

x³+2x²y+xy²

x²-xy-4x+4y

x²+2+2x-y²-4y-3

2) x-1/x-2+2x-3/x-2+x-4/x-2

2/3x+1/2x-2-x-4/6x²-6x

3) x³+5x²+4x+a chia hết cho đa thức x+5

Answer 1

x³ + 2x²y + xy²

= x(x² + 2xy + y²)

= x(x + y)²

x² - xy - 4x + 4y

= x(x - y) - 4(x - y)

= (x - y)(x - 4)

Answer 2

1.

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

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

\(\dfrac{x-1}{x-2}+\dfrac{2x-3}{x-2}+\dfrac{x-4}{x-2}\\ =\dfrac{4x-8}{x-2}=4\)

Answer 3

x³+2x²y+xy²

=x(x²+2xy+y²)

= x(x+y)²

x²-xy-4x+4y

=(x²-xy)-(4x-4y)

=x(x-y)-4(x-y)

=(x-y)(x-4)

Answer 4

1,x\(^3\)+2x\(^2\)y+xy\(^2\)

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

=x(x+y)\(^2\)

x\(^2\)-xy-4x+4y

=x(x-y)-4(x-y)

=(x-y)(x-4)

Answer 5

2,\(\dfrac{x-1}{x-2}\)+\(\dfrac{2x-3}{x-2}\)+\(\dfrac{x-4}{x-2}\)

=\(\dfrac{x-1+2x-3+x-4}{x-2}\)

=\(\dfrac{4x-8}{x-2}\)

=4