Phân tích đa thức thành nhân tử:
1. x bình - 3x + 2
2. 2x bình + 5x - 7
3. x bình + 7x - 8
4. x bình + 8x + 7
5. 2x bình - 5x - 7
Các bác giúp e vs, hứa sẽ tick, e cảm ơn nhiều!!!!!!!!!!!!!!
Phân tích các đa thức sau thành nhân tử :
a) 3x2 – 7x + 2;
b) a(x2 + 1) – x(a2 + 1).;
c)(x+2)(x+3)(x+4)(x+5)-24;
d)(a+1)(a+3)(a+5)(a+7)+15;
e)x2 + 2xy + 7x + 7y + y2 + 10
(x2 là x bình,y 2 là y bình,a2 là a bình nha)
Giúp mình với:33
a) 3x2 – 7x + 2
\(=3x^2-6x-x+2\)
\(=\left(3x^2-6x\right)-\left(x-2\right)\)
\(=3x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-1\right)\)
b) a(x2 + 1) – x(a2 + 1)
\(=ax^2+a-\left(a^2x+x\right)\)
\(=a\left(x^2+1\right)-x\left(a^2+1\right)\)
.......?
a) Ta có: \(3x^2-7x+2\)
\(=3x^2-6x-x+2\)
\(=3x\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-1\right)\)
b) Ta có: \(a\left(x^2+1\right)-x\left(a^2+1\right)\)
\(=x^2a+a-a^2x-x\)
\(=\left(x^2a-a^2x\right)+\left(a-x\right)\)
\(=xa\left(x-a\right)-\left(x-a\right)\)
\(=\left(x-a\right)\left(xa-1\right)\)
c) Ta có: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+120-24\)
\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+96\)
\(=\left(x^2+7x\right)^2+16\left(x^2+7x\right)+6\left(x^2+7x\right)+96\)
\(=\left(x^2+7x\right)\left(x^2+7x+16\right)+6\left(x^2+7x+16\right)\)
\(=\left(x^2+7x+16\right)\left(x^2+7x+6\right)\)
\(=\left(x^2+7x+16\right)\left(x+1\right)\left(x+6\right)\)
d) Ta có: \(\left(a+1\right)\left(a+3\right)\left(a+5\right)\left(a+7\right)+15\)
\(=\left(a^2+8a+7\right)\left(a^2+8a+15\right)+15\)
\(=\left(a^2+8a\right)^2+22\left(a^2+8a\right)+105+15\)
\(=\left(a^2+8a\right)^2+22\left(a^2+8a\right)+120\)
\(=\left(a^2+8a\right)^2+12\left(a^2+8a\right)+10\left(a^2+8a\right)+120\)
\(=\left(a^2+8a\right)\left(a^2+8a+12\right)+10\left(a^2+8a+12\right)\)
\(=\left(a^2+8a+12\right)\left(a^2+8a+10\right)\)
\(=\left(a+2\right)\left(a+6\right)\left(a^2+8a+10\right)\)
Phân tích đa thức thành nhân tử:
1. x bình - 5x - 6
2. 11x bình + 5x - 6
3. 1 + 3x + 2x bình
4. 6 - 2x - 8x bình
5. 7 - 4x - 3x bình
Các bác giúp e vs, hứa sẽ tick, e cảm ơn nhiều !!!!!!!!!!!!!!!!
Phân tích đa thức thành nhân tử:
1. x2 - 5x - 6
\(=x^2-6x+x-6\)
\(=\left(x^2-6x\right)+\left(x-6\right)\)
\(=x\left(x-6\right)+\left(x-6\right)\)
\(=\left(x+1\right)\left(x-6\right)\)
3. 1 + 3x + 2x2
\(=1+2x+x+2x^2\)
\(=\left(1+2x\right)+\left(x+2x^2\right)\)
\(=\left(1+2x\right)+x\left(1+2x\right)\)
\(=\left(1+2x\right)+\left(x+1\right)\)
4. 6 - 2x - 8x2
\(=6-8x+6x-8x^2\)
\(=\left(6+6x\right)-\left(8x+8x^2\right)\)
\(=6\left(1+x\right)-8x\left(1+x\right)\)
\(=\left(6-8x\right)\left(1+x\right)\)
5. 7 - 4x - 3x2
\(=7-7x+3x-3x^2\)
\(=\left(7-7x\right)+\left(3x-3x^2\right)\)
\(=7\left(1-x\right)+3x\left(1-x\right)\)
\(=\left(7+3x\right)\left(1-x\right)\)
1) \(x^2-5x-6\\ =x^2+x-6x-6\\ =x\left(x+1\right)-6\left(x+1\right)\\ =\left(x-6\right)\left(x+1\right)\)
3) \(1+3x+2x^2\\ =2x^2+2x+x+1\\ =2x\left(x+1\right)+\left(x+1\right)\\ =\left(x+1\right)\left(2x+1\right)\)
Tìm x biết:
1. x bình - 8x + 7 = 0
2. 5x bình -11x + 6 = 0
3. 2x bình - 3x + 1 = 0
4. x bình + 7x - 8 = 0
5. 3x bình + 7x - 10= 0
Các bác giúp e vs, hứa sẽ tick, e cảm ơn !!!!!!!!!!!!!!!!
1) \(x^2-8x+7=0\)
\(\Leftrightarrow x^2-7x-x+7=0\)
\(\Leftrightarrow\left(x^2-7x\right)-\left(x-7\right)=0\)
\(\Leftrightarrow x\left(x-7\right)-\left(x-7\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=7\end{matrix}\right.\)
2) \(5x^2-11x+6=0\)
\(\Leftrightarrow5x^2-5x-6x+6=0\)
\(\Leftrightarrow\left(5x^2-5x\right)-\left(6x-6\right)=0\)
\(\Leftrightarrow5x\left(x-1\right)-6\left(x-1\right)=0\)
\(\Leftrightarrow\left(5x-6\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5x-6=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{6}{5}\\x=1\end{matrix}\right.\)
3) \(2x^2-3x+1=0\)
\(\Leftrightarrow2x^2-2x-x+1=0\)
\(\Leftrightarrow\left(2x^2-2x\right)-\left(x-1\right)=0\)
\(\Leftrightarrow2x\left(x-1\right)-\left(x-1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\end{matrix}\right.\)
4) \(x^2+7x-8=0\)
\(\Leftrightarrow x^2+8x-x-8=0\)
\(\Leftrightarrow\left(x^2+8x\right)-\left(x+8\right)=0\)
\(\Leftrightarrow x\left(x+8\right)-\left(x+8\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-8\end{matrix}\right.\)
5) \(3x^2+7x-10=0\)
\(\Leftrightarrow3x^2-3x+10x-10=0\)
\(\Leftrightarrow\left(3x^2-3x\right)+\left(10x-10\right)=0\)
\(\Leftrightarrow3x\left(x-1\right)+10\left(x-1\right)=0\)
\(\Leftrightarrow\left(3x+10\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+10=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{10}{3}\\x=1\end{matrix}\right.\)
a: x^3-7x-6
=x^3-x-6x-6
=x(x-1)(x+1)-6(x+1)
=(x+1)(x^2-x-6)
=(x-3)(x+2)(x+1)
b: =2x^3+x^2-2x^2-x+6x+3
=x^2(2x+1)-x(2x+1)+3(2x+1)
=(2x+1)(x^2-x+3)
c: =2x^3-3x^2-2x^2+3x+2x-3
=x^2(2x-3)-x(2x-3)+(2x-3)
=(2x-3)(x^2-x+1)
d: =2x^3+x^2+2x^2+x+2x+1
=(2x+1)(x^2+x+1)
e: =3x^3+x^2-3x^2-x+6x+2
=(3x+1)(x^2-x+2)
f: =27x^3-9x^2-18x^2+6x+12x-4
=(3x-1)(9x^2-6x+4)
a) \(x^3-7x-6\)
\(=x^3-x-6x-6\)
\(=\left(x^3-x\right)-\left(6x+6\right)\)
\(=x\left(x^2-1\right)-6\left(x+1\right)\)
\(=x\left(x+1\right)\left(x-1\right)-6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x-6\right)\)
b) \(2x^3-x^2+5x+3\)
\(=2x^3+x^2-2x^2-x+6x+3\)
\(=\left(2x^3+x^2\right)-\left(2x^2+x\right)+\left(6x+3\right)\)
\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)
\(=\left(x^2-x+3\right)\left(2x+1\right)\)
c) \(2x^3-5x^2+5x+1\)
\(=2x^3-3x^2-2x^2+3x+2x-3\)
\(=\left(2x^3-3x^2\right)-\left(2x^2-3x\right)+\left(2x-3\right)\)
\(=x^2\left(2x-3\right)-x\left(2x-3\right)+\left(2x-3\right)\)
\(=\left(x^2-x+1\right)\left(2x-3\right)\)
d) \(2x^3+3x^2+3x+1\)
\(=2x^3+x^2+2x^2+x+2x+1\)
\(=\left(2x^3+x^2\right)+\left(2x^2+x\right)+\left(2x+1\right)\)
\(=x^2\left(2x+1\right)+x\left(2x+1\right)+\left(2x+1\right)\)
\(=\left(2x+1\right)\left(x^2+x+1\right)\)
e) \(3x^3-2x^2+5x+2\)
\(=3x^3+x^2-3x^2-x+6x+2\)
\(=\left(3x^3+x^2\right)-\left(3x^2+x\right)+\left(6x+2\right)\)
\(=x^2\left(3x+1\right)-x\left(3x+1\right)+2\left(3x+1\right)\)
\(=\left(3x-1\right)\left(x^2-x+2\right)\)
f) \(27x^3-27x^2+18x-4\)
\(=27x^3-9x^2-18x^2+6x+12x-4\)
\(=\left(27x^3-9x^2\right)-\left(18x^2-6x\right)+\left(12x-4\right)\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
Phân tích đa thức thành nhân tử:
1. x bình + 3x + 2
2. 3x bình + 2x - 1
3. x bình - 5x + 6
4. x bình - 5x + 6
5. x bình + 2x - 8
Các bác giúp e vs, hứa sẽ tick, e cảm ơn nhiều!!!!!!!!!!!!!!!!
1. \(x^2+3x+2=x^2+2x+x+2=x\left(x+2\right)+\left(x+2\right)=\left(x+2\right)\left(x+1\right)\)
2.
\(3x^2+2x-1=3x^2+3x-x-1=3x\left(x+1\right)-\left(x+1\right)=\left(x+1\right)\left(3x-1\right)\)3 và 4 bạn xem lại đề nha mik giải ko đc
5. \(x^2+2x-8=x^2+4x-2x-8=x\left(x+4\right)-2\left(x+4\right)=\left(x+4\right)\left(x-2\right)\)
3: \(x^2-5x+6=\left(x-2\right)\left(x-3\right)\)
4: \(x^2-5x+6=\left(x-2\right)\left(x-3\right)\)
mọi người giúp em bài này với :
Đề bài Phân tích đanh thức thành nhân tử
a) A= x^3 + x^2-x-1
b)B= x^3 - 3x^2 - 4x +12
c)C= -x^3 + 3x - 2
d)D= 2x^3 - x^2 - 8x + 4
e)E= -3x^3 + x^2 + 3x - 1
f)F= x^3 - 5x^3 + 2x + 8
g)G= x^3 - 5x^2 + 7x - 2
h)H= x^3 - x^2 - 5x -3
i)I= x^3 + 12x^2 + 6x + 7
Em cảm ơn mọi người nha !
a) \(A=\left(x^3+x^2\right)-\left(x+1\right)=x\left(x+1\right)-\left(x+1\right)=\left(x-1\right)\left(x+1\right)\)
b) \(B=\left(x^3-3x^2\right)-\left(4x-12\right)\)
\(=x^2\left(x-3\right)-4\left(x-3\right)=\left(x^2-4\right)\left(x-3\right)=\left(x-2\right)\left(x+2\right)\left(x-3\right)\)
a) A= x^3 + x^2-x-1
= (x^3 + x^2) - (x+1)
= x^2(x+1) - (x+1)
= (x^2 -1) (x+1)
b)B= x^3 - 3x^2 - 4x +12
= (x^3 - 3x^2) - (4x - 12)
= x^2(x-3) - 4(x-3)
= (x^2 -4)(x-3)
c)C= -x^3 + 3x - 2
=
d)D= 2x^3 - x^2 - 8x + 4
= (2x^3 - x^2) - (8x -4)
= x^2(2x -1) - 4(2x -1)
= (x^2 -4) (2x-1)
= (x-2)(x+2)(2x-1)
đến đây thôi
Phân tích các đa thức sau thành p.tử:
a, 2x^2 + 5x + 2
b, x^3 + 5x^2 +8x + 4
c, x^3 - 9x^2 +6x +16
d, 2x^3 + 3x^2 +3x + 1
e, 2x^3 - 5x^2 + 5x - 3
MONG BẠN NÀO TỐT BỤNG GIÚP MÌNH
CẢM ƠN RẤT NHIỀU =)
AI LÀM MÌNH SẼ K ĐÚNG + 1 THẺ KHÓA HỌC T.ANH GIAO TIẾP
\(a.2x^2+5x+2=2x^2+4x+x+2=\left(x+2\right)\left(2x+1\right)\)
Phân tích đa thức thành nhân tử
1) 4x^2 + 5x-6
2)5x^2-18x-8
3)2x^2+3x-ư7
4)7x^2+3xy-10y^2
5)x^2+5x-2
6)x^8+x^7+1
1) 4x2 + 5x - 6 = 4x2 + 8x - 3x - 6 = 4x( x + 2 ) - 3( x + 2 ) = ( x + 2 )( 4x - 3 )
2) 5x2 - 18x - 8 = 5x2 - 20x + 2x - 8 = 5x( x - 4 ) + 2( x - 4 ) = ( x - 4 )( 5x + 2 )
3) 2x2 + 3x - 27 = 2x2 - 6x + 9x - 27 = 2x( x - 3 ) + 9( x - 3 ) = ( x - 3 )( 2x + 9 ) < đã sửa ._. >
4) 7x2 + 3xy - 10y2 = 7x2 - 7xy + 10xy - 10y2 = 7x( x - y ) + 10y( x - y ) = ( x - y )( 7x + 10y )
5) x2 + 5x - 2 < sai đề ._. >
6) x8 + x7 + 1 = x8 + x7 + x6 - x6 + 1
= ( x8 + x7 + x6 ) - ( x6 - 1 )
= x6( x2 + x + 1 ) - ( x3 - 1 )( x3 + 1 )
= x6( x2 + x + 1 ) - ( x - 1 )( x2 + x + 1 )( x3 + 1 )
= ( x2 + x + 1 )[ x6 - ( x - 1 )( x3 + 1 ) ]
= ( x2 + x + 1 )( x6 - x4 + x3 - x + 1 )
. Help Me ! Please :)) Mik đang gấp lắm nhé nên nếu các bạn biết thì giải giúp mik nhé :3 Cảm ơn nhiều nhiều lắm nek ~~~ Bạn nào làm đúng mik sẽ tik nhé =))
~ ĐỀ BÀI: Phân tích các đa thức sau thành nhân tử
1) (x^2+x+1) . (x^2+x+2) - 12
2) (x+2) . (x+3) . (x+4) . (x+5) - 24
3) x^2+2xy+y^2-x-y-12
4) x^3 + 2x - 3
5) x^3 + 5x^2 + 8x + 4
6) 6x^2 - 11x + 3
7) 2x^2 + 3x - 27
8) 2x^2 - 5xy - 3y^2
1) \(\left(x^2+x+1\right)\left(x^2+x+2\right)-12=x^4+x^3+2x^2+x^3+x^2+2x+x^2+x+2-12\)
\(=x^4+2x^3+4x^2+3x-10=\left(x^4+2x^3\right)+\left(4x^2+8x\right)+\left(-5x-10\right)\)
\(=x^3.\left(x+2\right)+4x.\left(x+2\right)-5.\left(x+2\right)=\left(x+2\right)\left(x^3+4x-5\right)\)
\(=\left(x+2\right)\left(x^3-x^2+x^2-x+5x-5\right)=\left(x+2\right)\left(x-1\right)\left(x^2+x+5\right)\)
2) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left[\left(x+2\right)\left(x+5\right)\right].\left[\left(x+3\right)\left(x+4\right)\right]-24\)
\(=\left(x^2+7x+10\right).\left(x^2+7x+12\right)-24\)
Đặt \(a=x^2+7x+10\) thì ta có :\(a.\left(a+2\right)-24=a^2+2a-24=\left(a^2+2a+1\right)-25=\left(a+1\right)^2-5^2\)
\(=\left(a+1+5\right)\left(a+1-5\right)=\left(a+6\right)\left(a-4\right)\)
Thay a , ta có :
\(\left(x^2+7x+10+6\right)\left(x^2+7x+10-4\right)=\left(x^2+7x+16\right).\left(x^2+x+6x+6\right)\)
\(=\left(x^2+7x+16\right)\left(x+1\right)\left(x+6\right)\)