(x3 - 7x + 3 - x2) : (x - 3)
(x3 – 7x + 3 – x2) : (x – 3) = (x3 – x2 – 7x + 3) : (x – 3)
\(\left(3x-7x+3-2x\right):\left(x-3\right)=\left(3x-2x-7x+3\right):\left(x-3\right)\)
\(\left(3-6x\right):\left(x-3\right)-\left(3-6x\right):\left(x-3\right)=0\)
\(0=0\)
vậy \(x\in\varnothing\)
Theo mình thì x\(\ne\)3 thì hai vế bằng nhau
Thực hiện phép chia:
a) ( x 3 - 3x - 2) : (x - 2);
b) ( x 3 + 6 x 2 + 8x - 3): ( x 2 + 3x -1);
c) (2 x 4 – 7 x 3 + 9 x 2 - 7x + 2): (2 x 2 - 5x + 2).
a) x 2 + 2x + 1. b) x + 3. c) x 2 – x + 1.
a) A = -3x(x-5) +3( x2 -4x) -3x-10
b) B = 4x( x2 -7x +2) – 4( x3 -7x2 +2x -5)
c) C = 5x( x2 – x) – x2( 5x-5) -15
d) D = 7( x2 -5x+3)- x( 7x-35) -14
e) E = x2 - 4x - x( x-4) -15
A = - 3\(x\).(\(x-5\)) + 3(\(x^2\) - 4\(x\)) - 3\(x\) - 10
A = - 3\(x^2\) + 15\(x\) + 3\(x^2\) - 12\(x\) - 3\(x\) - 10
A = (- 3\(x^2\) + 3\(x^2\)) + (15\(x\) - 12\(x\) - 3\(x\)) - 10
A = 0 + (3\(x-3x\)) - 10
A = 0 - 10
A = - 10
Phân tích các đa thức sau thành nhân tử:
1) x3 - 7x + 6
2) x3 - 9x2 + 6x + 16
3) x3 - 6x2 - x + 30
4) 2x3 - x2 + 5x + 3
5) 27x3 - 27x2 + 18x - 4
6) x2 + 2xy + y2 - x - y - 12
7) (x + 2)(x +3)(x + 4)(x + 5) - 24
8) 4x4 - 32x2 + 1
9) 3(x4 + x2 + 1) - (x2 + x + 1)2
10) 64x4 + y4
11) a6 + a4 + a2b2 + b4 - b6
12) x3 + 3xy + y3 - 1
13) 4x4 + 4x3 + 5x2 + 2x + 1
14) x8 + x + 1
15) x8 + 3x4 + 4
16) 3x2 + 22xy + 11x + 37y + 7y2 +10
17) x4 - 8x + 63
Chia nhỏ ra cậu ơi :v
Cậu đặt câu hỏi free nên đặt nhỏ ra thì mới có người làm nha để như này dày cộp không ai dám làm đou =(((
Tìm x biết:
a/ 5x( x- 3) = x – 3 b/ x3 - x = 0 c/ x2 – 7x + 6 = 0
d/ x2 – 4 + ( x – 2)2 = 0 e/ x2 – 16 –( x +4) = 0 f/ x2 + x – 2 = 0
a: \(\Leftrightarrow\left(x-3\right)\left(5x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{1}{5}\end{matrix}\right.\)
b: \(\Leftrightarrow x\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)
Giải các phương trình sau:
a, (9x2 - 4)(x + 1) = (3x +2)(x2 - 1)
b, (x - 1)2 - 1 + x2 = (1 - x)(x + 3)
c, (x2 - 1)(x + 2)(x - 3) = (x - 1)(x2 - 4)(x + 5)
d, x4 + x3 + x + 1 = 0
e, x3 - 7x + 6 = 0
f, x4 - 4x3 + 12x - 9 = 0
g, x5- 5x3 + 4x = 0
h, x4 - 4x3 + 3x2 + 4x - 4 = 0
a, \(\Leftrightarrow\left(9x^2-4\right)\left(x+1\right)-\left(3x+2\right)\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(\left(9x^2-4\right)-\left(\left(3x+2\right)\left(x-1\right)\right)\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(9x^2-4-\left(3x^2-x-2\right)\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(9x^2-4-3x^2+x+2\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(3x^2+x-2\right)=0\)
\(\Leftrightarrow\left(x+1\right)=0;3x^2+x-2=0\)
=> x=-1
với \(3x^2+x-2=0\)
ta sử dụng công thức bậc 2 suy ra : \(x=\dfrac{2}{3};x=-1\)
Vậy ghiệm của pt trên \(S\in\left\{-1;\dfrac{2}{3}\right\}\)
b: \(\Leftrightarrow x^2-2x+1-1+x^2=x+3-x^2-3x\)
\(\Leftrightarrow2x^2-2x=-x^2-2x+3\)
\(\Leftrightarrow3x^2=3\)
hay \(x\in\left\{1;-1\right\}\)
c: \(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x+2\right)\left(x-3\right)-\left(x-1\right)\left(x-2\right)\left(x+2\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left[\left(x+1\right)\left(x-3\right)-\left(x-2\right)\left(x+5\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left(x^2-2x-3-x^2-3x+10\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left(-5x+7\right)=0\)
hay \(x\in\left\{1;-2;\dfrac{7}{5}\right\}\)
Biểu diễn đa thức A = B.Q + R trong đó Q, R là đa thức chia và đa thức dư trong phép chia A cho B.
a) A = x 3 - 4 x 2 - 12x và B = x + 2;
b) A = x 3 - 3 x 2 + 39x - 6 và B = x 2 - 5x +1;
c) A = 3 x 3 + 7 x 2 - 7x + 3 - 3 và B = 3 x 2 - 2x - 1.
a) A = ( x 2 – 6x)B.
b) A = (-x – 8)B + 2
c) A = (x + 3)B + 6.
Với giá trị x thỏa mãn 2 x 2 – 7x + 3 = 0, tính giá trị phân thức:
a) x 2 − 2 x + 1 2 x 2 − x − 1 ; b) x 3 − 27 x 2 − 2 x − 3 .
Bài 1:Phân tích đa thức thành nhân tử:
a) x3y+x-y-1
b) x2.(x-2)+4.(2-x)
c) x3-x2-20x
d) (x2+1)2-(x+1)2
e) 6x2-7x+2
f) x4+8x2+12
g) (x3+x+1).(x3+x)-2
h) (x+1).(x+2).(x+3).(x+4)-1
i) -(x2+2)2+4x.(x2+2)-3x2
j) -(x2+2)2+4x.(x2+2).3x2
k) -(x2+2)2+4x.(x2+2)+3x2
l) 81x4+4y4
Giúp với ạa
a) x³y + x - y - 1
= (x³y - y) + (x - 1)
= y(x³ - 1) + (x - 1)
= y(x - 1)(x² + x + 1) + (x - 1)
= (x - 1)[y(x² + x + 1) + 1]
= (x - 1)(x²y + xy + y + 1)
b) x²(x - 2) + 4(2 - x)
= x²(x - 2) - 4(x - 2)
= (x - 2)(x² - 4)
= (x - 2)(x - 2)(x + 2)
= (x - 2)²(x + 2)
c) x³ - x² - 20x
= x(x² - x - 20)
= x(x² + 4x - 5x - 20)
= x[(x² + 4x) - (5x + 20)]
= x[x(x + 4) - 5(x + 4)]
= x(x + 4)(x - 5)
d) (x² + 1)² - (x + 1)²
= (x² + 1 - x - 1)(x² + 1 + x + 1)
= (x² - x)(x² + x + 2)
= x(x - 1)(x² + x + 2)
e) 6x² - 7x + 2
= 6x² - 3x - 4x + 2
= (6x² - 3x) - (4x - 2)
= 3x(2x - 1) - 2(2x - 1)
= (2x - 1)(3x - 2)
f) x⁴ + 8x² + 12
= x⁴ + 2x² + 6x² + 12
= (x⁴ + 2x²) + (6x² + 12)
= x²(x² + 2) + 6(x² + 2)
= (x² + 2)(x² + 6)
g) (x³ + x + 1)(x³ + x) - 2
Đặt u = x³ + x
x³ + x + 1 = u + 1
(u + 1).u - 2
= u² + u - 2
= u² - u + 2u - 2
= (u² - u) + (2u - 2)
= u(u - 1) + 2(u - 1)
= (u - 1)(u + 2)
= (x³ + x - 1)(x³ + x + 2)
= (x³ + x - 1)(x³ + x² - x² - x + 2x + 2)
= (x³ + x - 1)[(x³ + x²) - (x² + x) + (2x + 2)]
= (x³ + x - 1)[x²(x + 1) - x(x + 1) + 2(x + 1)]
= (x³ + x - 1)(x - 1)(x² - x + 2)
h) (x + 1)(x + 2)(x + 3)(x + 4) - 1
= [(x + 1)(x + 4)][(x + 2)(x + 3)] - 1
= (x² + 5x + 4)(x² + 5x + 6) - 1 (1)
Đặt u = x² + 5x + 4
u + 2 = x² + 5x + 6
(1) u.(u + 2) - 1
= u² + 2u - 1
= u² + 2u + 1 - 2
= (u² + 2u + 1) - 2
= (u + 1)² - 2
= (u + 1 + √2)(u + 1 - √2)
= (x² + 5x + 4 + 1 + √2)(x² + 5x + 4 + 1 - √2)
= (x² + 5x + 5 + √2)(x² + 5x + 5 - √2)
i: \(-\left(x^2+2\right)^2+4x\left(x^2+2\right)-3x^2\)
\(=-\left[\left(x^2+2\right)^2-4x\left(x^2+2\right)+3x^2\right]\)
\(=-\left[\left(x^2+2\right)^2-x\left(x^2+2\right)-3x\left(x^2+2\right)+3x^2\right]\)
\(=-\left[\left(x^2+2\right)\left(x^2+2-x\right)-3x\left(x^2+2-x\right)\right]\)
\(=-\left(x^2+2-x\right)\left(x^2-3x+2\right)\)
\(=-\left(x+2\right)\left(x-1\right)\left(x-2\right)\left(x-1\right)\)
\(=-\left(x+2\right)\left(x-2\right)\left(x-1\right)^2\)
l: \(81x^4+4y^4\)
\(=81x^4+36x^2y^2+4y^4-36x^2y^2\)
\(=\left(81x^4+36x^2y^2+4y^4\right)-\left(6xy\right)^2\)
\(=\left[\left(9x^2\right)^2+2\cdot9x^2\cdot2y^2+\left(2y^2\right)^2\right]-\left(6xy\right)^2\)
\(=\left(9x^2+2y^2\right)^2-\left(6xy\right)^2\)
\(=\left(9x^2+2y^2+6xy\right)\left(9x^2+2y^2-6xy\right)\)