Bài 2 : Phân tích các đa thức sau thành nhân tử :
a, x^2 + 7x + 12
b, 3x^2 - 8x + 5
c, x^4 + 5x^2 - 6
d, x^4 - 34x^2 + 225
e, x^2 - 5xy + 6y^2
f, 4x^2 - 17xy + 13y^2
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26 tháng 2 2020
a)\(=\left(x-2\right)\left(5x-3x^2\right)\)
\(=x\left(x-2\right)\left(5-3x\right)\)
b)\(=\left(4x-x^2-4\right)\left(4x+x^2+4\right)\)
\(=-\left(x^2-4x+4\right)\left(x+2\right)^2\)
=\(-\left(x-2\right)^2\left(x+2\right)^2\)
c)\(\left(=5x^2-5xy\right)+\left(7y-7x\right)\)
\(=-5x\left(y-x\right)+7\left(y-x\right)\)
\(=\left(y-x\right)\left(7-5x\right)\)
d)\(=\left(3x^2-6x\right)-\left(2x-4\right)\)
\(=3x\left(x-2\right)-2\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-2\right)\)
e)\(=[\left(x^2\right)^2+8^2+2.x^2.8]-2.8.x^2\)
\(=\left(x^2+8\right)^2-16x^2\)
\(=\left(x^2+8-4x\right)\left(x^2+8+4x\right)\)
__Chúc bạn hc tốt ......
PA
30 tháng 10 2016
(x - 4)(x2 + 4x + 16) - x(x2 - 6) = 2
x3 - 64 - x3 + 6x = 2
6x = 2 + 64
6x = 66
x = 66 : 6
x = 11
x3 - 27 + 3x(x - 3)
= (x - 3)(x2 + 3x + 9) + 3x(x - 3)
= (x - 3)(x2 + 3x + 9 + 3x)
= (x - 3)(x2 + 6x + 9)
= (x - 3)(x + 3)2
5x3 - 7x2 + 10x - 14
= 5x(x2 + 2) - 7(x2 + 2)
= (x2 + 2)(5x - 7)
BC
22 tháng 9 2019
Bạn tải ứng dụng PhotoMath về nha. Ứng dụng này sẽ giải toán số chi tiết
C
22 tháng 9 2019
a) \(x^3-4x^2-12x+27\)
\(=\left(x^3+27\right)-\left(4x^2+12x\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
b) \(x^3-3x^2-4x+12\)
\(=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x^2-4\right)\left(x-3\right)\)
\(=\left(x+2\right)\left(x-2\right)\left(x-3\right)\)
a) \(9x^2+6xy+y^2=\left(3x+y\right)^2\)
b) \(6x-9-x^2=-\left(x-3\right)^2\)
4 tháng 8 2020
Bài 4:
a) Ta có: \(a^4+a^2+1\)
\(=a^4+2a^2+1-a^2\)
\(=\left(a^2+1\right)^2-a^2\)
\(=\left(a^2-a+1\right)\left(a^2+a+1\right)\)
b) Ta có: \(a^4+a^2-2\)
\(=a^4+2a^2-a^2-2\)
\(=a^2\left(a^2+2\right)-\left(a^2+2\right)\)
\(=\left(a^2+2\right)\left(a^2-1\right)\)
\(=\left(a^2+2\right)\left(a-1\right)\left(a+1\right)\)
c) Ta có: \(x^4+4x^2-5\)
\(=x^4+5x^2-x^2-5\)
\(=x^2\left(x^2+5\right)-\left(x^2+5\right)\)
\(=\left(x^2+5\right)\left(x^2-1\right)\)
\(=\left(x^2+5\right)\left(x-1\right)\left(x+1\right)\)
d) Ta có: \(x^3-19x-30\)
\(=x^3-25x+6x-30\)
\(=x\left(x^2-25\right)+6\left(x-5\right)\)
\(=x\left(x-5\right)\left(x+5\right)+6\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2+5x\right)+6\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2+5x+6\right)\)
\(=\left(x-5\right)\left(x^2+2x+3x+6\right)\)
\(=\left(x-5\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x-5\right)\left(x+2\right)\left(x+3\right)\)
e) Ta có: \(x^3-7x-6\)
\(=x^3-4x-3x-6\)
\(=x\left(x^2-4\right)-3\left(x+2\right)\)
\(=x\left(x-2\right)\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-2x\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-2x-3\right)\)
\(=\left(x+2\right)\left(x^2-3x+x-3\right)\)
\(=\left(x+2\right)\left[x\left(x-3\right)+\left(x-3\right)\right]\)
\(=\left(x+2\right)\left(x-3\right)\left(x+1\right)\)
f) Ta có: \(x^3-5x^2-14x\)
\(=x\left(x^2-5x-14\right)\)
\(=x\left(x^2-7x+2x-14\right)\)
\(=x\left[x\left(x-7\right)+2\left(x-7\right)\right]\)
\(=x\left(x-7\right)\left(x+2\right)\)
6 tháng 8 2020
a, ( x2 + x )2 - 14 ( x2 + x ) + 24
= (x2 + x)2 - 2(x2 + x) -12(x2 + x) + 24
= (x2 + x).(x2 + x -2) - 12(x2 + x -2)
= (x2 + x -2).(x2 + x -12)
= (x2 + 2x - x - 2).(x2 + 4x - 3x - 12)
=[x.(x+2)-(x+2)].[x.(x+4)-3(x+4)]
= (x+2).(x-1).(x+4).(x-3)
= x4 + 2x3 - 13x2 - 14x + 24
b, ( x2 + x )2 + 4x2 + 4x - 12
= x4 + 2x3 + x2 + 4x2 + 4x -12
= x4 + 2x3 + 5x2 + 4x -12
c, x4 + 2x3 + 5x2 + 4x - 12
= x4 - x3 + 3x3 - 3x2 + 8x2 - 8x +12x -12
= x3(x-1) + 3x2(x-1) + 8x(x-1) + 12(x-1)
= (x-1) . (x3 + 3x2 + 8x +12)
= (x-1) . ( x3 +2x2 + x2 + 2x + 6x +12)
= (x-1). [x2(x+2) + x(x+2) + 6(x+2)]
= (x-1).(x+2).(x2 + x+ 6)
18 tháng 7 2017
b ) Ta có : 3x2 - 7x - 6
= 3x2 - 9x + 2x - 6
= 3x (x - 3) + 2(x - 3)
= (x - 3)(3x + 2)
CW
15 tháng 7 2016
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
=
Bài 2 : Phân tích các đa thức sau thành nhân tử :
a, x2 + 7x + 12
= x2 + 3x + 4x + 12
= x(x + 3) + 4(x + 3)
= (x + 3)(x + 4)
b, 3x2 - 8x + 5
= 3x2 - 3x - 5x + 5
= 3x(x - 1) - 5(x - 1)
= (x - 1)(3x - 5)
c, x4 + 5x2 - 6
= x4 - x2 + 6x2 - 6
= x2(x2 - 1) + 6(x2 - 1)
= (x2 - 1)(x2 + 6)
= (x - 1)(x + 1)(x2 + 6)
d, x4 - 34x2 + 225
= x4 - 9x2 - 25x2 + 225
= x2(x2 - 9) - 25(x2 - 9)
= (x2 - 9)(x2 - 25)
= (x - 3)(x + 3)(x - 5)(x + 5)
e, x2 - 5xy + 6y2
= x2 + xy - 6xy + 6y2
= x(x + y) - 6y(x + y)
= (x + y)(x - 6y)
f, 4x2 - 17xy + 13y2
= 4x2 - 4xy - 13xy + 13y2
= 4x(x - y) - 13y(x - y)
= (x - y)(4x - 13y)
Mình cảm ơn bạn nha ❤🙆♀️