Question

Phân tích các đa thức thành nhân tử

a) + + 23x + 15

b) ( + 3x + 1) ( + 3x - 3) - 5

c) (6x - 5) (6x - 3) - 5

d) + + + 6x + 1

e) \(x^4\) + \(5x^2\) + 9

f) \(x^4\) + \(2010x^2\) + 2009x + 2010

g) \(\left(x+2009\right)^3\) + \(\left(x-2010\right)^2\) - 1

Answer 1

1)

$x^3+9x^2+23x+15=(x^3+x^2)+(8x^2+8x)+(15x+15)$

$=x^2(x+1)+8x(x+1)+15(x+1)$

$=(x+1)(x^2+8x+15)$

$=(x+1)[(x^2+3x)+(5x+15)]$

$=(x+1)[x(x+3)+5(x+3)]=(x+1)(x+3)(x+5)$

5)

$x^4+5x^2+9=(x^4+6x^2+9)-x^2$

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

Answer 2

2)

$(x^2+3x+1)(x^2+3x-3)-5$

$=(a+1)(a-3)-5$ (đặt $x^2+3x=a$)

$=a^2-2a-8$

$=a^2+2a-(4a+8)=a(a+2)-4(a+2)=(a-4)(a+2)$

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

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

$=[x(x-1)+4(x-1)][x(x+1)+2(x+1)]=(x+4)(x-1)(x+2)(x+1)$

Answer 3

3)

$(3x-2)^2(6x-5)(6x-3)-5$

$=(9x^2-12x+4)(36x^2-48x+15)-5$

$=(9x^2-12x+4)[4(9x^2-12x)+15]-5$

$=(a+4)(4a+15)-5$ (đặt $9x^2-12x=a$)

$=4a^2+31a+55$

$=4a^2+20a+11a+55$

$=4a(a+5)+11(a+5)=(4a+11)(a+5)=(36x^2-48x+11)(9x^2-12x+5)$

$=

Answer 4

4)

$x^4+6x^3+11x^2+6x+1$

$=(x^4+6x^3+9x^2)+2x^2+6x+1$

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

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

Answer 5

6)

$x^4+2010x^2+2009x+2010$

$=(x^4-x)+2010x^2+2010x+2010$

$=x(x^3-1)+2010(x^2+x+1)$

$=x(x-1)(x^2+x+1)+2010(x^2+x+1)$

$=(x^2+x+1)(x^2-x+2010)$

7) Biểu thức không phân tích được thành nhân tử.