Phân tích các đa thức sau thành nhân tử
a) x2 - 7
b) x2 - \(2\sqrt{2}\) x +2
c) x2 + \(2\sqrt{13}\) x +13
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Khách
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Những câu hỏi liên quan
27 tháng 9 2021
a) \(=x^4-14x^2+40-72=x^4-14x^2-32=\left(x-4\right)\left(x+4\right)\left(x^2+2\right)\)
b) \(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)+1=\left(x^2+5x\right)^2+2\left(x^2+5x\right)+1=\left(x^2+5x+1\right)^2\)
c) \(=x^4+3x^3-3x^2+3x^3+9x^2-9x+x^2+3x-3-5=x^4+6x^3+7x^2-6x-8=\left(x-1\right)\left(x+1\right)\left(x+2\right)\left(x+4\right)\)
27 tháng 9 2021
a: Ta có: \(\left(x^2-4\right)\left(x^2-10\right)-72\)
\(=x^4-14x^2-32\)
\(=\left(x^2-16\right)\left(x^2+2\right)\)
\(=\left(x-4\right)\left(x+4\right)\left(x^2+2\right)\)
b: Ta có: \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1\)
\(=\left(x^2+5x+6\right)\left(x^2+5x+4\right)+1\)
\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24+1\)
\(=\left(x^2+5x+1\right)^2\)
25 tháng 8 2021
a) \(x^2\left(x^2+4\right)-x^2-4=x^2\left(x^2+4\right)-\left(x^2+4\right)=\left(x^2+4\right)\left(x^2-1\right)=\left(x^2+4\right)\left(x-1\right)\left(x+1\right)\)
b) \(\left(x^2+x\right)^2+4x^2+4x-12=\left(x^2+x\right)^2+4\left(x^2+x\right)+4-16=\left(x^2+x+2\right)^2-4^2=\left(x^2+x+2-4\right)\left(x^2+x+2+4\right)=\left(x^2+x-2\right)\left(x^2+x+6\right)=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24=\left(x^2+7x+10\right)^2+2\left(x^2+7x+10\right)+1-25=\left(x^2+7x+11\right)^2-5^2=\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)=\left(x^2+7x+6\right)\left(x^2+7x+16\right)=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
NT
25 tháng 8 2021
a. \(x^2\left(x^2+4\right)-x^2-4\)
\(=x^2\left(x^2+4\right)-\left(x^2+4\right)\)
\(=\left(x^2-1\right)\left(x^2+4\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+4\right)\)
b. \(\left(x^2+x\right)^2+4x^2+4x-12\)
\(=x^4+2x^3+5x^2+4x-12\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
c. \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\) (*)
Đặt \(t=x^2+7x+10\), ta được
(*) \(=t\left(t+2\right)-24\)
\(=t^2+2t-24\)
\(=\left(t-4\right)\left(t+6\right)\)
hay \(\left(x^2+7x+6\right)\left(x^2+7x+18\right)\)
NI
28 tháng 10 2021
a) \(x^2+2xy+y^2-4=\left(x+y\right)^2-2^2\)
\(=\left(x+y-2\right)\left(x+y+2\right)\)
b) \(x^2-y^2+x+y=\left(x-y\right)\left(x+y\right)+1\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+1\right)\)
c) \(y^2+x^2+2xy-16=x^2+2xy+y^2-16\)
\(=\left(x+y\right)^2-4^2=\left(x+y+4\right)\left(x+y-4\right)\)
TL
3
18 tháng 11 2021
\(a,=3xyz\left(x+2\right)\\ b,=5\left(x+2\right)-x\left(x+2\right)=\left(x+2\right)\left(5-x\right)\\ c,=\left(x+y\right)^2-z^2=\left(x+y-z\right)\left(x+y+z\right)\)
18 tháng 11 2021
a) 3x2yz + 6xyz = 3xyz(x+2)
b) 5(x+2) - x2 - 2x = 5(x+2) - x(x+2) = (5+x)(x+2)
c) x2 + 2xy + y2 - 22 = (x2+2xy+y2) - 22 = (x+y)2 - 22 = (x+y+2)(x+y-2)
TM
11 tháng 8 2021
a/ \(\left(x+y\right)^2-8\left(x+y\right)+12\)
\(=\left(x+y\right)\left(x+y-8+12\right)\)
\(=\left(x+y\right)\left(x+y+4\right)\)
==========
b/\(\left(x^2+2x\right)^2-2x^2-4x-3\)
\(=\left(x^2+2x\right)^2-\left(2x^2+4x\right)-3\)
\(=\left(x^2+2x\right)^2-2\left(x^2+2x\right)-3\)
\(=\left(x^2+2x\right)\left(x^2+2x-5\right)\)
===========
c/ \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)
\(=\left(x^2+x\right)\left(x^2+x-2-15\right)\)
\(=\left(x^2+x\right)\left(x^2+x-17\right)\)
[---]
LL
1
15 tháng 9 2021
\(a,=\left(x-1\right)^4-2\left(x-1\right)^2+1\\ =\left[\left(x-1\right)^2-1\right]^2\\ =\left(x^2-2x-2\right)^2\\ b,=\left[\left(x+1\right)\left(x+5\right)\right]\left[\left(x+2\right)\left(x+4\right)\right]-4\\ =\left(x^2+6x+5\right)\left(x^2+6x+8\right)-4\\ =\left(x^2+6x\right)^2+13\left(x^2+6x\right)+36\\ =\left(x^2+6x+4\right)\left(x^2+6x+9\right)\\ =\left(x+3\right)^2\left(x^2+6x+4\right)\)
LP
4 tháng 9 2021
\(a.6x^3y^2.\left(2-x\right)+9x^2y^2.\left(x-2\right)\\ =6x^3y^2.\left(2-x\right)-9x^2y^2.\left(2-x\right)\\ =3x^2y^2\left(2-x\right)\left(2x-3\right)\)
AH
Akai Haruma
Giáo viên
4 tháng 9 2021
Lời giải:
a.
$=6x^3y^2(2-x)-9x^2y^2(2-x)$
$=(2-x)(6x^3y^2-9x^2y^2)$
$=(2-x).3x^2y^2(2x-3)=3x^2y^2(2-x)(2x-3)$
b.
$=(x^2-y^2)-(4x-4y)=(x-y)(x+y)-4(x-y)$
$=(x-y)(x+y-4)$
c.
$81x^2-(9y^2-6yz+z^2)$
$=(9x)^2-(3y-z)^2=(9x-3y+z)(9x+3y-z)$
AH
Akai Haruma
Giáo viên
25 tháng 10 2021
a.
$x^2-y^2-2x+2y=(x^2-y^2)-(2x-2y)=(x-y)(x+y)-2(x-y)=(x-y)(x+y-2)$
b.
$x^2(x-1)+16(1-x)=x^2(x-1)-16(x-1)=(x-1)(x^2-16)=(x-1)(x-4)(x+4)$
c.
$x^2+4x-y^2+4=(x^2+4x+4)-y^2=(x+2)^2-y^2=(x+2-y)(x+2+y)$
d.
$x^3-3x^2-3x+1=(x^3+1)-(3x^2+3x)=(x+1)(x^2-x+1)-3x(x+1)$
$=(x+1)(x^2-4x+1)$
AH
Akai Haruma
Giáo viên
25 tháng 10 2021
e.
$x^4+4y^4=(x^2)^2+(2y^2)^2+2.x^2.2y^2-4x^2y^2$
$=(x^2+2y^2)^2-(2xy)^2=(x^2+2y^2-2xy)(x^2+2y^2+2xy)$
f.
$x^4-13x^2+36=(x^4-4x^2)-(9x^2-36)$
$=x^2(x^2-4)-9(x^2-4)=(x^2-9)(x^2-4)=(x-3)(x+3)(x-2)(x+2)$
g.
$(x^2+x)^2+4x^2+4x-12=(x^2+x)^2+4(x^2+x)-12$
$=(x^2+x)^2-2(x^2+x)+6(x^2+x)-12$
$=(x^2+x)(x^2+x-2)+6(x^2+x-2)=(x^2+x-2)(x^2+x+6)$
$=[x(x-1)+2(x-1)](x^2+x+6)=(x-1)(x+2)(x^2+x+6)$
h.
$x^6+2x^5+x^4-2x^3-2x^2+1$
$=(x^6+2x^5+x^4)-(2x^3+2x^2)+1$
$=(x^3+x^2)^2-2(x^3+x^2)+1=(x^3+x^2-1)^2$
PH
3
17 tháng 9 2021
a) \(49-x^2-y^2+2xy=49-\left(x^2-2xy+y^2\right)=49-\left(x-y\right)^2=\left(7-x+y\right)\left(7+x-y\right)\)
b) \(\left(x-3\right)+2x\left(3-x\right)^2=\left(x-3\right)+2x\left(x-3\right)^2=\left(x-3\right)\left[1+2x\left(x-3\right)\right]=\left(x-3\right)\left(2x^2-6x+1\right)\)
a) x2- 7= \(\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)\)
b) \(x^2-2\sqrt{2}x+2=\left(x-\sqrt{2}\right)^2\)
c) \(x^2+2\sqrt{13}x+13=\left(x+\sqrt{13}\right)^2\)