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a) \(6x^2-x-1\)
\(=6x^2-3x+2x-1\)
\(=3x\left(2x-1\right)+\left(2x-1\right)\)
\(=\left(3x+1\right)\left(2x-1\right)\)
a) \(x^3-x^2-4=x^3-2x^2+x^2-4=x^2\left(x-2\right)+\left(x-2\right)\left(x+2\right)=\left(x-2\right)\left(x^2+x+2\right)\)
b) \(x^3-5x^2+8x-4=x^3-x^2-4x^2+4x+4x-4=x^2\left(x-1\right)-4x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-4x+4\right)=\left(x-1\right)\left(x-2\right)^2\)
c) \(2x^3-12x^2+17x-2=2x^3-4x^2-8x^2+16x+x-2=2x^2\left(x-2\right)-8x\left(x-2\right)+\left(x-2\right).\)
\(=\left(x-2\right)\left(2x^2-8x+1\right)\)
d) \(2x^4+x^3-22x^2+15x+36=2x^4+2x^3-x^3-x^2-21x^2-21x+36x+36.\)
\(=2x^3\left(x+1\right)-x^2\left(x+1\right)-21x\left(x+1\right)+36\left(x+1\right)\)
\(=\left(x+1\right)\left(2x^3-x^2-21x+36\right)\)
\(a=15x^3+x^2-mx+n\)
\(=5x\left(x^2+2x-1\right)-3\left(3x^2+2x-1\right)-\left(m-1\right)x-3+n\)
\(\frac{a}{3x^2+2x-1}=5x-3-\frac{\left(m-1\right)x+\left(3-n\right)}{3x^2+2x-1}\)
=> để chia hết : m=1; n=3
a)
$6x^2-x-x=6x^2-3x+2x-1=3x(2x-1)+(2x-1)=(2x-1)(3x+1)$
b)
$6x^2-6x-3=3(2x^2-2x-1)$
c)
$15x^2-2x-1=15x^2-5x+3x-1=5x(3x-1)+(3x-1)=(3x-1)(5x+1)$
d)
$2x^3-x^2+5x+3=2x^3+x^2-2x^2-x+6x+3$
$=x^2(2x+1)-x(2x+1)+3(2x+1)=(2x+1)(x^2-x+3)$
e)
$2x^3-5x^2+5x-3=2x^3-3x^2-2x^2+3x+2x-3$
$=x^2(2x-3)-x(2x-3)+(2x-3)=(2x-3)(x^2-x+1)$
a)
$6x^2-x-x=6x^2-3x+2x-1=3x(2x-1)+(2x-1)=(2x-1)(3x+1)$
b)
$6x^2-6x-3=3(2x^2-2x-1)$
c)
$15x^2-2x-1=15x^2-5x+3x-1=5x(3x-1)+(3x-1)=(3x-1)(5x+1)$
d)
$2x^3-x^2+5x+3=2x^3+x^2-2x^2-x+6x+3$
$=x^2(2x+1)-x(2x+1)+3(2x+1)=(2x+1)(x^2-x+3)$
e)
$2x^3-5x^2+5x-3=2x^3-3x^2-2x^2+3x+2x-3$
$=x^2(2x-3)-x(2x-3)+(2x-3)=(2x-3)(x^2-x+1)$
\(x^3+x^2+9x-10x^2-10x+25x+25\)
\(=x^2\left(x+1\right)-10x\left(x+1\right)+25\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-10x+25\right)=\left(x+1\right)\left(x-5\right)^2\)
a) = 4x2 + 10x + 35 (dư 104)
b) = 3x3 - 7x2 + 14x - 24 (dư 47)
c) = 12x3 + 22x2 + 44x + 73 (dư 156)
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