phân tích đa thức thành nhân tử: a) x^3+x^2-4x-4 b) (x-3)^2 – (2-3x)^2 c) x^2-2x-15 d) 5x^3-5x^2y-10x^2+10xy Thực hiện phép tính : x^2+2x/2x+10 + x-5

Giải thích các bước giải:

Bài 1:

a.Ta có:

$x^3+x^2-4x-4$ 

$=(x^3+x^2)-(4x+4)$ 
$=x^2(x+1)-4(x+1)$

$=(x+1)(x^2-4)$

$=(x+1)(x-2)(x+2)$

b.Ta có:

$(x-3)^2-(2-3x)^2$

$=((x-3)-(2-3x))((x-3)+(2-3x))$

$=(x-3-2+3x)(x-3+2-3x)$

$=(4x-5)(-2x-1)$

c.Ta có:
$x^2-2x-15$

$=(x^2-2x+1)-16$

$=(x-1)^2-4^2$

$=(x-1-4)(x-1+4)$

$=(x-5)(x+3)$

d.Ta có:

$5x^3-5x^2y-10x^2+10xy$

$=(5x^3-5x^2y)-(10x^2-10xy)$

$=5x^2(x-y)-10x(x-y)$

$=5x(x-y)(x-2)$

Bài 2 :

Ta có:

$\dfrac{x^2+2x}{2x+10}+\dfrac{x-5}{x}+\dfrac{50-5x}{2x(x+5)}$

$=\dfrac{x^2+2x}{2\left(x+5\right)}+\dfrac{x-5}{x}+\dfrac{50-5x}{2x\left(x+5\right)}$

$=\dfrac{\left(x^2+2x\right)x}{2\left(x+5\right)x}+\dfrac{\left(x-5\right)\cdot \:2\left(x+5\right)}{x\cdot \:2\left(x+5\right)}+\dfrac{50-5x}{2x\left(x+5\right)}$

$=\dfrac{\left(x^2+2x\right)x+\left(x-5\right)\cdot \:2\left(x+5\right)+50-5x}{2x\left(x+5\right)}$

$=\dfrac{x\left(x^2-5+4x\right)}{2x\left(x+5\right)}$

$=\dfrac{x^2-5+4x}{2\left(x+5\right)}$

$=\dfrac{\left(x-1\right)\left(x+5\right)}{2\left(x+5\right)}$

$=\dfrac{x-1}{2}$