Thực hiện phép chia:
a) ( x 3 - 2 x 2 - 15x + 36) : (x + 4);
b) ( 2 x 4 + 2 x 3 + 3 x 2 - 5x - 20) : ( x 2 + x + 4);
c) (2 x 3 + 11 x 2 + 18x-3) : (2x + 3);
d) (2x3 + 9x2 +5x + 41) : (2x2 - x + 9).
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`a, (4x^3y^2 - 8x^2y + 10xy) : 2xy`
`= 2x^2y - 4x + 5`.
`b, 7x^4y^2 - 2x^2y^2 - 5x^3y^4 : 3x^2y`
`= 7/3 x^2y - 3/2y - 5/3xy^3`
`a, (5ab - 2a^2):a`
`= 5b - 2a`
`b, (6x^2y^2-xy^2+3x^2y) : (-3xy)`
`= -2xy + y/3 - x`.
`a, 20x^3y^5 : 5x^2y^2`
`= (20:5)x^(3-2) . y^(5-2)`
`= 4xy^3`
`b, 18x^3y^5 : (3(-x^3)y^2)`
`= -(18:3)y^(5-3)`
`= -6y^2`
Thực hiện phép chia:
a) (-y^2):y^4=\(\dfrac{-1}{y^2}\)
b) (-x)^5:(-x)^3=(-x)^2
a) (-y2) : y4=\(\dfrac{-1}{y^2}\)
b) (-x)5 : (-x)3 = (-x)2
\(a,\Rightarrow x\left(x+3\right)-\left(x-3\right)\left(x+3\right)=0\\ \Rightarrow\left(x+3\right)\left(x-x+3\right)=0\\ \Rightarrow3\left(x+3\right)=0\Rightarrow x=-3\\ b,A:B=\left(2x^2-x+4x-2\right):\left(2x-1\right)\\ =\left[x\left(2x-1\right)+2\left(2x-1\right)\right]:\left(2x-1\right)\\ =x+2\)
Đáp án:
a.3x³−5x²+7xa.3x³−5x²+7x
b.−4x²y−10x²y+2xyb.−4x²y−10x²y+2xy
c.−x³+2x²+29x+20c.−x³+2x²+29x+20
d.2x⁴−3x³+2x²+3x−4d.2x⁴−3x³+2x²+3x−4
e.x²−4y²e.x²−4y²
h.2x²−6x+13h.2x²−6x+13
g.3xy⁴−12y²+2x²yg.3xy⁴−12y²+2x²y
f.−2x²y³+y−3f.−2x²y³+y−3
Giải thích các bước giải:
a.3x.(x²−5x+7)a.3x.(x²−5x+7)
=3x³−5x²+7x=3x³−5x²+7x
b.−2xy.(2x³+5x−1)b.−2xy.(2x³+5x−1)
=−4x⁴y−10xy²+2xy=−4x⁴y−10xy²+2xy
c.(x+4).(−x²+6x+5)c.(x+4).(−x²+6x+5)
=−x³+6x²+5x−4x²+24x+20=−x³+6x²+5x−4x²+24x+20
=−x³+2x²+29x+20=−x³+2x²+29x+20
d.(x²−1).(2x²−3x+4)d.(x²−1).(2x²−3x+4)
=2x⁴−3x³+4x²−2x²+3x−4=2x⁴−3x³+4x²−2x²+3x−4
=2x⁴−3x³+2x2+3x−4=2x⁴−3x³+2x2+3x−4
e.(x+2y).(x−2y)e.(x+2y).(x−2y)
=x²−(2y)²=x²−(2y)²
=x²−4y²=x²−4y²
h.(3x−1)²−7(x²+2)h.(3x−1)²−7(x²+2)
=9x²−6x+1−7x²−14=9x²−6x+1−7x²−14
=2x²−6x+13=2x²−6x+13
g.(6x²g.(6x²y⁵−xy³+4x³y²):2xy−xy³+4x³y²):2xy
=3xy⁴−12y²+2x²y=3xy⁴−12y²+2x²y
f.(−12x³y⁴+6xy²−18xy):6xyf.(−12x³y⁴+6xy²−18xy):6xy
=−2x³y³+y−3
\(a,=\dfrac{5x+30+x^2-30}{x\left(x+6\right)}=\dfrac{x\left(x+5\right)}{x\left(x+6\right)}=\dfrac{x+5}{x+6}\\ b,=\dfrac{3x^2+4x+1-x^2+2x-1-x^2-2x+3}{\left(x-1\right)^2\left(x+1\right)}\\ =\dfrac{x^2+4x+3}{\left(x-1\right)^2\left(x+1\right)}=\dfrac{\left(x+1\right)\left(x+3\right)}{\left(x-1\right)^2\left(x+1\right)}=\dfrac{x+3}{\left(x-1\right)^2}\)
\(c,=\dfrac{3x^2+2x+1+x^2-2x+1-2x^2-2x-2}{\left(x-1\right)\left(x^2+x+1\right)}\\ =\dfrac{2x^2-2x}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{2x}{x^2+x+1}\)
c: \(=\dfrac{\left(x-5\right)\left(x+5\right)}{3x+4}\cdot\dfrac{-5}{x-5}=\dfrac{-5\left(x+5\right)}{3x+4}\)
a) Đa thức thương x 2 – 6x + 9.
b) Đa thức thương 2 x 2 – 5.
c) Đa thức thương x 2 + 4x + 3 và đa thức dư -12.
d) Đa thức x + 5 và đa thức dư x – 4.