Phân tích đa thức thành nhân tử
a,3x^3-x^2-21x+7
b,x^3-4x^2+8x-8
C,x^3-5x^2-5x+1
Phân tích đa thức thành nhân tử
a,3x^3-x^2-21x+7
b,x^3-4x^2+8x-8
C,x^3-5x^2-5x+1
a.\(3x^3-x^2-21x+7=\)\(x^2\left(3x-1\right)-7\left(3x-1\right)=\left(3x-1\right)\left(x^2-7\right)\)
b.\(x^3-4x^2+8x-8=\left(x^3-8\right)+\left(-4x^2+8x\right)\)=\(\left(x-2\right)\left(x^2+2x+4\right)\)\(-\)\(4x\left(x-2\right)\)
=\(\left(x-2\right)\left(x^2-2x+4\right)\)
c.\(x^3-5x^2-5x+1\)=\(\left(x^3+1\right)-\left(5x^2+5x\right)\)=\(\left(x+1\right)\left(x^2-x+1\right)-5x\left(x+1\right)\)
=\(\left(x+1\right)\left(x^2-6x+1\right)\)
Phân tích đa thức thành các nhân tử:
a)x^2-(a+b)x+ab
b)7x^3-3xyz-21x^2+9z
c)4x+4y-x^2(x+y)
d)y^2+y-x^2+x
e)4x^2-2x-y^2-y
f)9x^2-25y^2-6x+10y
Phân tích đa thức thành nhân tử
a)(5x-4)(4x-5)-(x-3)(x-2)-(5x-4)(3x-2)
b)(5x-4)(4x-5)+(5x-1)(x+4)+3(3x-2)(4-5x)
c)(5x-4)^2+(16-25x^2)+(5x-4)(3x+2)
d)x^4-x^3-x+1
e)x^6-x^4+2x^3+2x^2
a)x^2-(a+b)x+ab
= x^2 - ax - bx + ab
= (x^2 - ax) - (bx - ab)
= x(x-a) - b(x-a)
= (x-b)(x-a)
b)7x^3-3xyz-21x^2+9z
=
c)4x+4y-x^2(x+y)
= 4(x + y) - x^2(x+y)
= (4-x^2) (x+y)
= (2-x)(2+x)(x+y)
d) y^2+y-x^2+x
= (y^2 - x^2) + (x+y)
= (y-x)(y+x)+ (x+y)
= (y-x+1) (x+y)
e)4x^2-2x-y^2-y
= [(2x)^2 - y^2] - (2x +y)
= (2x-y)(2x+y) - (2x+y)
= (2x -y -1)(2x+y)
f)9x^2-25y^2-6x+10y
=
BT3: Phân tích các đa thức sau thành nhân tử bằng phương pháp cách tách hạng tử. a, x^3 + 4x^2 - 21x b, 5x^3 + 6x^2 + x c, x^3 - 7x + 6 d, 3x^3 + 2x - 5
a) \(x^3+4x^2-21x\)
\(=x\left(x^2+4x-21\right)\)
\(=x\left(x^2-3x+7x-21\right)\)
\(=x\left[x\left(x-3\right)+7\left(x-3\right)\right]\)
\(=x\left(x-3\right)\left(x+7\right)\)
b) \(5x^3+6x^2+x\)
\(=x\left(5x^2+6x+1\right)\)
\(=x\left(5x^2+5x+x+1\right)\)
\(=x\left[5x\left(x+1\right)+\left(x+1\right)\right]\)
\(=x\left(x+1\right)\left(5x+1\right)\)
c) \(x^3-7x+6\)
\(=x^3+2x^2-3x-2x^2-4x+6\)
\(=x\left(x^2+2x-3\right)-2\left(x^2+2x-3\right)\)
\(=\left(x-2\right)\left(x^2+2x-3\right)\)
\(=\left(x-2\right)\left(x-1\right)\left(x+3\right)\)
d) \(3x^3+2x-5\)
\(=3x^3+3x^2+5x-3x^2-3x-5\)
\(=x\left(3x^2+3x+5\right)-\left(3x^2+3x+5\right)\)
\(=\left(x-1\right)\left(3x^2+3x+5\right)\)
Phân tích đa thức thành nhân tử
a,3x^3-x^2-21x+7
b,x^3-4x^2+8x-8
C,x^3-5x^2-5x+1
\(a,3x^3-x^2-21x+7\)
\(=x^2\left(3x-1\right)-7\left(3x-1\right)\)
\(=\left(3x-1\right)\left(x^2-7\right)\)
\(b,x^3-4x^2+8x-8\)
\(=\left(x^3-8\right)-4x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+4\right)-4x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x+4-4x\right)\)
\(=\left(x-2\right)\left(x^2-2x+4\right)\)
\(c,x^3-5x^2-5x+1\)
\(=\left(x^2+1\right)-5x\left(x+1\right)\)
=\(\left(x+1\right)\left(x^2-x+1\right)-5x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1-5x\right)=\left(x+1\right)\left(x^2-4x+1\right)\)
Phân tích đa thức thành nhân tử(tách hạng tử)
1)x^2+2x-3
2)x^2-5x+6
3)x^2+7x^2+12x
4)x^2-x-12
5)3x^2+3x-36
6)5x^2-5x-10
7)3x^2-7x-6
8)4x^2+4x-3
9)8x^2-2x-3
Phân tích đa thức thành nhân tử(tách hạng tử)
1)x^2+2x-3=x^2-x+3x-3=x(x-1)+3(x-1)=(x-1)(x+3)
2)x^2-5x+6=x^2-2x-3x+6=x(x-2)-3(x-2)=(x-2)(x-3)
3)x^2+7x+12=(x+3)(x+4)
4)x^2-x-12=(x-4)(x+3)
5)3x^2+3x-36=3[(x-3)(x+4)]
6)5x^2-5x-10=5[(x-2)(x+1) ]
7)3x^2-7x-6=(x-3)(3x+2)
8)4x^2+4x-3=4x^2+6x-2x-3=(2x-1)(2x+3)
9)8x^2-2x-3=8x^2+4x-6x-3=(4x-3)(2x+1)
1: \(x^2+2x-3=\left(x+3\right)\left(x-1\right)\)
2: \(x^2-5x+6=\left(x-2\right)\left(x-3\right)\)
3: \(x^2+7x^2+12x=4x\left(2x+3\right)\)
4: \(x^2-x-12=\left(x-4\right)\left(x+3\right)\)
5: \(3x^2+3x-36=3\left(x^2+x-12\right)=3\left(x+4\right)\left(x-3\right)\)
6: \(5x^2-5x-10=5\left(x^2-x-2\right)=5\left(x-2\right)\left(x+1\right)\)
Phân tích đa thức thành nhân tử
A= 6x^4-5x^3+4x^2+2x-1
B=4x^4+4x^3+5x^2+8x-6
C=x^4+x^3-5x^2+x-6
A = 6x4 - 5x3 + 4x2 + 2x - 1
= 6x4 + 3x3 - 8x3 - 4x2 + 8x2 + 4x - 2x - 1
= 3x3. ( 2x + 1 ) - 4x2 ( 2x + 1 ) + 4x ( 2x + 1 ) - ( 2x + 1 )
= ( 2x + 1 ) ( 3x3 - 4x2 + 4x - 1 )
= ( 2x + 1 ) ( 3x3 - x2 - 3x2 + x + 3x - 1 )
= ( 2x + 1 ) [ x2 ( 3x - 1 ) - x ( 3x - 1 ) + ( 3x - 1 ) ]
= ( 2x + 1 ) ( 3x - 1 ) ( x2 - x + 1 )
B = 4x4 + 4x3 + 5x2 + 8x - 6
= 4x4 - 2x3 + 6x3 - 3x2 + 8x2 - 4x + 12x - 6
= 2x3 ( 2x - 1 ) + 3x2 ( 2x - 1 ) + 4x ( 2x - 1 ) + 6 ( 2x - 1 )
= ( 2x - 1 ) ( 2x3 + 3x2 + 4x + 6 )
= ( 2x - 1 ) [ x2 ( 2x + 3 ) + 2 ( 2x + 3 ) ]
= ( 2x - 1 ) ( 2x + 3 ) ( x2 + 2 )
C = x4 + x3 - 5x2 + x - 6
= x4 - 2x3 + 3x3 - 6x2 + x2 - 2x + 3x - 6
= x3 ( x - 2 ) + 3x2 ( x - 2 ) + x ( x - 2 ) + 3 ( x - 2 )
= ( x - 2 ) ( x3 + 3x2 + x + 3 )
= ( x - 2 ) [ x2 ( x + 3 ) + ( x + 3 ) ]
= ( x - 2 ) ( x + 3 ) ( x2 + 1 )
Phân tích đa thức thành nhân tử
1) 4x^4+4x^3+5x^2+2x+1
2) x^8+x+1
3) x^8+3x^4+4
4) 3x^2+22xy+11x+37y+7^2+10
5) x^4-8x+63
Phân tích đa thức thành nhân tử:
1)5x^2-4x;
2)8x^2(x-3y)-12x(x-3y);
3)3(x-y)-5x(y-x)
1. 5x2 - 4x
= x(5x - 4)
2. 8x2(x - 3y) - 12x(x - 3y)
= (8x2 - 12x)(x - 3y)
= 4x(2x - 3)(x - 3y)
3. 3(x - y) - 5x(y - x)
= 3(x - y) + 5x(x - y)
= (3 + 5x)(x - y)
Phân tích các đa thức sau thành nhân tử:
a) 4x4 - 21x2y2 + y4
b) x5 - 5x3 + 4x
c) x3 + 5x2 + 3x - 9
d) x16 + x8 - 2
\(4x^4-21x^2y^2+y^4\)
\(=\left(4x^4+4x^2y^2+y^4\right)-25x^2y^2\)
\(=\left(2x^2+y^2\right)^2-\left(5xy\right)^2\)
\(=\left(2x^2+y^2-5xy\right)\left(2x^2+y^2+5xy\right)\)
\(x^5-5x^3+4x\)
\(=x\left(x^4-5x^2+4\right)\)