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a,A(\(x\)) = 13\(x^4\) + 3\(x^2\) + 15\(x\) - 8\(x\) - 7 - 7\(x\) + 7\(x^2\) - 10\(x^4\)
A(\(x\)) = (13\(x^4\) - 10\(x^4\)) + (3\(x^2\) + 7\(x^2\)) + (15\(x\) - 8\(x\) - 7\(x\)) - 7
A(\(x\)) = 3\(x^4\) + 10\(x^2\) + 0 - 7
A(\(x\)) = 3\(x^4\) + 10\(x^2\) - 7
B(\(x\)) = -4\(x^4\) - 10\(x^2\) + 10 + 5\(x^4\) - 3\(x\) - 18 + 30 - 5\(x^2\)
B(\(x\)) = (-4\(x^4\) + 5\(x^4\)) - (10\(x^2\) + 5\(x^2\)) - 3\(x\) + (10 + 30 - 18)
B(\(x\)) = \(x^4\) - 15\(x^2\) - 3\(x\) + 22
b,C(\(x\)) = A(\(x\)) + B(\(x\)) = 3\(x^4\) + 10\(x^2\) - 7 + \(x^4\) - 15\(x^2\) - 3\(x\) + 22
C(\(x\)) = 4\(x^4\) - (15\(x^2\) - 10\(x^2\)) - 3\(x\) + 22
C(\(x\)) = 4\(x^4\) - 5\(x^2\) - 3\(x\) + 15
c, D(\(x\)) = B(\(x\)) - A(\(x\)) = \(x^4\) - 15\(x^2\) - 3\(x\) + 22 - 3\(x^4\) - 10\(x^2\) + 7
D(\(x\)) = (\(x^4\) - 3\(x^4\)) - (15\(x^2\) + 10\(x^2\)) + (22 + 7)
D(\(x\)) = - 2\(x^4\) - 25\(x^2\) + 29
d, Thay \(x\) = 1 vào C(\(x\)) ta có: C(1) = 4.14 - 5.12 -3.1 + 15 = 11 (xem lại đề bài em nhá)
a: \(=\dfrac{x^4-6x^3+12x^2-14x+3}{x^2-4x+1}\)
\(=\dfrac{x^4-4x^3+x^2-2x^3+8x^2-2x+3x^2-12x+3}{x^2-4x+1}\)
\(=x^2-2x+3\)
b: \(=\dfrac{x^5-3x^4+5x^3-x^2+3x-5}{x^2-3x+5}=x^2-1\)
c: \(=\dfrac{2x^4-5x^3+2x^2+2x-1}{x^2-x-1}\)
\(=\dfrac{2x^4-2x^3-2x^2-3x^3+3x^2+3x+x^2-x-1}{x^2-x-1}\)
\(=2x^2-3x+1\)
a) \(x^2-4=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=-2\end{cases}}\)
\(A=x^3-3x^2+3x-1=\left(x-1\right)^3\)
Với x=2 thì: \(A=\left(2-1\right)^3=1\)
Với x=-2 thì \(A=\left(-2-1\right)^3=-3^3=-27\)
b) \(x^2+5x-6=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+6\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=-6\end{cases}}\)
\(B=x^3-3x^2+3x-1=\left(x-1\right)^3\)
Với x=1 thì \(A=\left(1-1\right)^3=0\)
Với x=-6 thì \(A=\left(-6-1\right)^3=-7^3=-343\)
\(\text{⇔(x−1)(x+6)=0}\)chỗ đó s ra thế bn ?? mìh chưa hiểu
Câu 1:
\(\dfrac{x^2-10x+21}{x^3-7x^2+x-7}=\dfrac{\left(x-7\right)\left(x-3\right)}{\left(x-7\right)\left(x^2+1\right)}=\dfrac{x-3}{x^2+1}\)
\(\dfrac{2x^2-x-15}{2x^3+5x^2+2x+5}=\dfrac{2x^2-6x+5x-15}{\left(2x+5\right)\left(x^2+1\right)}=\dfrac{\left(2x+5\right)\left(x-3\right)}{\left(2x+5\right)\left(x^2+1\right)}=\dfrac{x-3}{x^2+1}\)
Do đó: \(\dfrac{x^2-10x+21}{x^3-7x^2+x-7}=\dfrac{2x^2-x-15}{2x^3+5x^2+2x+5}\)
1, \(\left(2x^4-5x^2y^2+3xy^3\right)\left(5x^3+x^2y-y^3\right)\)
\(=10x^7-25x^5y^2+15x^4y^3+2x^6y-5x^4y^3+5x^2y^5+3xy^6\)
2, a, \(4-2x+5x^2-4x^2\&5x-3+x^2\)
Sắp xếp: \(4-2x+5x^2-4x^2=5x^2-4x^2-2x+4=x^2-2x+4\)
\(5x-3+x^2=x^2+5x-3\)
- \(\left(x^2-2x+4\right)\left(x^2+5x-3\right)=x^4+3x^3-9x^2-14x-12\)
b, Làm tương tự câu a
1 ) \(\left(2x^4-5x^2y^2+3xy^3\right)\left(5x^3+x^2y-y^3\right)\)
\(=2x^4\left(5x^3+x^2y-y^3\right)-5x^2y^2\left(5x^3+x^2y-y^3\right)+3xy^3\left(5x^3+x^2y-y^3\right)\)\(=10x^7+2x^6y-2x^4y-25x^5y^2-5x^4y^3+5x^2y^5+15x^4y^3+3x^3y^4-3xy^6\)2 ) a ) \(4-2x+5x^2-4x^2=x^2-2x+4\)
\(5x-3+x^2=x^2+5x-3\)
\(\left(x^2-2x+4\right)\left(x^2+5x-3\right)\)
\(=x^4-2x^3+4x^2+5x^3-10x^2+20x-3x^2+6x-12\)
\(=x^4+3x^3-9x^2+26x-12\)
b ) \(10-x^4+3x-4x^2=-x^4-4x^2+3x+10\)
\(2x+x^3-1=x^3+2x-1\)
\(\left(-x^4-4x^2+3x+10\right)\left(x^3+2x-1\right)\)
\(=-x^4\left(x^3+2x-1\right)-4x^2\left(x^3+2x-1\right)+3x\left(x^3+2x-1\right)+10\left(x^3+2x-1\right)\)\(=-x^7-2x^5+x^4-4x^5-8x^3+4x^2+3x^4+6x^2-3x+10x^3+20x-10\)\(=-x^7-\left(2x^5+4x^5\right)+\left(3x^4+x^4\right)+\left(10x^3-8x^3\right)+\left(4x^2+6x^2\right)+\left(20x-3x\right)-10\)\(=-x^7-6x^5+4x^4+2x^3+10x^2+17x-10\)
Bài 1 :
b, Ta có : \(4x^2-25-\left(2x-5\right)\left(2x+7\right)\)
\(=\left(2x-5\right)\left(2x+5\right)-\left(2x-5\right)\left(2x+7\right)\)
\(=\left(2x-5\right)\left(2x+5-2x-7\right)\)
\(=-2\left(2x-5\right)\)
c, Ta có : \(x^3+27+\left(x+3\right)\left(x-9\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)\)
\(=\left(x+3\right)\left(x^2-3x+9+x-9\right)\)
\(=x\left(x+3\right)\left(x-2\right)\)
Bài 2 :
a, Để \(x^3+3x^2+3x-2⋮x+1\)
<=> \(x^3+1+3x^2+3x-3⋮x+1\)
<=> \(\left(x+1\right)^3-3⋮x+1\)
Ta thấy : \(\left(x+1\right)^3⋮x+1\)
<=> \(-3⋮x+1\)
<=> \(x+1\inƯ_{\left(3\right)}\)
<=> \(x+1=\left\{1,-1,3,-3\right\}\)
<=> \(x=\left\{0,-2,2,-4\right\}\)
Vậy ...
b, Để \(2x^2+x-7⋮x-2\)
<=> \(2x^2-8x+8+9x-15⋮x-2\)
<=> \(2\left(x-2\right)^2+9x-15⋮x-2\)
Ta thấy : \(2\left(x-2\right)^2⋮x-2\)
<=> \(9x-15⋮x-2\)
<=> \(9x-18+3⋮x-2\)
Ta thấy : \(8\left(x-2\right)⋮x-2\)
<=> \(3⋮x-2\)
<=> \(x-2\inƯ_{\left(3\right)}\)
<=> \(x-2=\left\{1,-1,3,-3\right\}\)
<=> \(x=\left\{3,1,5,-1\right\}\)
Vậy ...
`@` `\text {Ans}`
`\downarrow`
`1,`
`a)`
\(A(x) = 5x^5 + 2 - 7x - 4x^2 - 2x^5\)
`= (5x^5 - 2x^5) - 4x^2 - 7x + 2`
`= 3x^5 - 4x^2 - 7x + 2`
`b)`
`A(x)+B(x)`
`=`\((3x^5 - 4x^2 - 7x + 2)+(-3x^5 + 4x^2 + 3x - 7)\)
`= 3x^5 - 4x^2 - 7x + 2-3x^5 + 4x^2 + 3x - 7`
`= (3x^5 - 3x^5) + (-4x^2 + 4x^2) + (-7x + 3x) + (2-7)`
`= -4x - 5`
`b)`
`A(x) - B(x)`
`= 3x^5 - 4x^2 - 7x + 2 + 3x^5 - 4x^2 - 3x + 7`
`= (3x^5 + 3x^5) + (-4x^2 - 4x^2) + (-7x - 3x) + (2+7)`
`= 6x^5 - 8x^2 - 10x + 9`
`c)`
Thay `x=-1` vào đa thức `A(x)`
` 3*(-1)^5 - 4*(-1)^2 - 7*(-1) + 2`
`= 3*(-1) - 4*1 + 7 + 2`
`= -3 - 4 + 7 + 2`
`= -7+7 + 2`
`= 2`
Bạn xem lại đề ;-;.
`2,`
`M =` \(( 3 x - 2 )( 2 x + 1 )-( 3 x + 1 )( 2 x - 1 )\)
`= 3x(2x+1) - 2(2x+1) - [3x(2x-1) + 2x - 1]`
`= 6x^2 + 3x - 4x - 2 - (6x^2 - 3x + 2x - 1)`
`= 6x^2 - x - 2 - (6x^2 - x - 1)`
`= 6x^2 - x - 2 - 6x^2 + x + 1`
`= (6x^2 - 6x^2) + (-x+x) + (-2+1)`
`= -1`
Vậy, giá trị của biểu thức không phụ thuộc vào giá trị của biến.
2:
M=6x^2+3x-4x-2-6x^2+3x-2x+1
=-1
1;
a: A(x)=3x^5-4x^2-7x+2
b: B(x)=-3x^5+4x^2+3x-7
B(x)+A(x)
=-3x^5-4x^2-7x+2+3x^5+4x^2+3x-7
=-4x-5
A(x)-B(x)
=-3x^5-4x^2-7x+2-3x^5-4x^2-3x+7
=-6x^5-8x^2-10x+9