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a) a4 + a2 - 2
a4 + 2a2 - a2 - 2
a2.( a2 + 2 ) - ( a2 + 2 )
( a2 - 1 ).( a2 + 2 )
( a + 1 ).( a - 1 ).( a2 +2 )
b) x4 + 4x2 - 5
x4 + 5x2 - x2 - 5
x2.( x2 + 5 ) - ( x2 + 5 )
( x2 - 1 ).( x2 + 5 )
( x + 1 ).( x - 1 ).( x2 + 5 )
c) x3 - 19x - 30
x3 + 2x2 - 2x2 + 4x - 15x - 30
x2( x + 2 ) - 2x.( x + 2 ) - 15.( x + 2 )
( x + 2 ).( x2 - 2x - 15 )
d) x3 - 7x - 6
x3 - 3x2 + 3x2 - 9x + 2x - 6
x2.( x - 3 ) + 3x.( x - 3 ) + 2.( x - 3 )
( x - 3 ).( x2 + 3x +2 )
( x - 3 ).( x2 + 2x + x + 2 )
( x - 3 ).( x.( x + 2 ) + ( x + 2 )
( x + 1 ).( x + 2 ).( x - 3 )
e) x3 - 5x2 - 14x
x3 - 7x2 + 2x2 - 14x
x2.( x - 7 ) + 2x.( x - 7 )
( x - 7 ).( x2 + 2x )
x.( x + 2 ).( x - 7 )
a)x7+x5+1=x7+x6-x6+2x5-x5+x4-x4+x3-x3+x2-x2+1
=x7-x6+x5-x3+x2+x6-x5+x4-x2+x+x5-x4+x3-x+1
=x2(x5-x4+x3-x+1)+x(x5-x4+x3-x+1)+1(x5-x4+x3-x+1)
=(x2+x+1)(x5-x4+x3-x+1)
b)4x4-32x2+1=4x4+12x3+2x2-12x3-36x2-6x+2x2+6x+1
=2x2(2x2+6x+1)-6x(2x2+6x+1)+1(2x2+6x+1)
=(2x2-6x+1)(2x2+6x+1)
c)x6+27=(x2+3)(x2-3x+3)(x2+3x+3)
d)3(x4+x2+1)-(x2+x+1)
=3x4-3x3+2x2+3x3-3x2+2x+3x2-3x+2
=x2(3x2-3x+2)+x(3x2-3x+2)+1(3x2-3x+2)
=(x2+x+1)(3x2-3x+2)
e)bạn tự làm nhé
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: \(x^3-5x^2-14x\)
\(=x\left(x^2-5x-14\right)\)
\(=x\left(x^2-7x+2x-14\right)\)
\(=x\left[x\left(x-7\right)+2\left(x-7\right)\right]\)
\(=x\left(x-7\right)\left(x+2\right)\)
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)
a) Ta có: \(x^2+4x+3\)
\(=x^2+x+3x+3\)
\(=x\left(x+1\right)+3\left(x+1\right)\)
\(=\left(x+1\right)\left(x+3\right)\)
b) Ta có: \(16x-5x^2-3\)
\(=-5x^2+16x-3\)
\(=-5x^2+15x+x-3\)
\(=-5x\left(x-3\right)+\left(x-3\right)\)
\(=\left(x-3\right)\left(-5x+1\right)\)
c) Ta có: \(2x^2+7x+5\)
\(=2x^2+2x+5x+5\)
\(=2x\left(x+1\right)+5\left(x+1\right)\)
\(=\left(x+1\right)\left(2x+5\right)\)
d) Ta có: \(2x^2+3x-5\)
\(=2x^2+5x-2x-5\)
\(=x\left(2x+5\right)-\left(2x+5\right)\)
\(=\left(2x+5\right)\left(x-1\right)\)
e) Ta có: \(x^3-3x^2+1-3x\)
\(=\left(x+1\right)\cdot\left(x^2-x+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1-3x\right)\)
\(=\left(x+1\right)\left(x^2-4x+1\right)\)
f) Ta có: \(x^2-4x-5\)
\(=x^2-4x+4-9\)
\(=\left(x-2\right)^2-3^2\)
\(=\left(x-2-3\right)\left(x-2+3\right)\)
\(=\left(x-5\right)\left(x+1\right)\)
g) Ta có: \(\left(a^2+1\right)^2-4a^2\)
\(=\left(a^2+1\right)^2-\left(2a\right)^2\)
\(=\left(a^2+1-2a\right)\left(a^2+1+2a\right)\)
\(=\left(a-1\right)^2\cdot\left(a+1\right)^2\)
h) Ta có: \(x^3-3x^2-4x+12\)
\(=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-4\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
i) Ta có: \(x^4+x^3+x+1\)
\(=x^3\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+1\right)\)
\(=\left(x+1\right)^2\cdot\left(x^2-x+1\right)\)
k) Ta có: \(x^4-x^3-x^2+1\)
\(=x^3\left(x-1\right)-\left(x^2-1\right)\)
\(=x^3\left(x-1\right)-\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x^3-x-1\right)\)
l) Ta có: \(\left(2x+1\right)^2-\left(x-1\right)^2\)
\(=\left(2x+1-x+1\right)\left(2x+1+x-1\right)\)
\(=3x\left(x+2\right)\)
m) Ta có: \(x^4+4x^2-5\)
\(=x^4-x^2+5x^2-5\)
\(=x^2\left(x^2-1\right)+5\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
a) \(x^2-xz-9y^2+3yz\)
\(=\left(x^2-9y^2\right)-\left(xz-3yz\right)\)
\(=\left[x^2-\left(3y\right)^2\right]-z\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y\right)-z\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y-z\right)\)
b) \(x^3-x^2-5x+125\)
\(=\left(x^3+125\right)-\left(x^2+5x\right)\)
\(=\left(x^3+5^3\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-5x+5^2\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-5x+5^2-x\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
c) \(x^3+2x^2-6x-27\)
\(=\left(x^3-27\right)-\left(2x^2-6x\right)\)
\(=\left(x^3-3^3\right)-2x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+3x+3^2\right)-2x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+3x+3^2-2x\right)\)
\(=\left(x-3\right)\left(x^2+x+9\right)\)
e) \(4x^4+4x^3-x^2-x\)
\(=4x^3\left(x+1\right)-x\left(x+1\right)\)
\(=\left(x+1\right)\left(4x^3-x\right)\)
f) \(x^6-x^4-9x^3+9x^2\)
\(=x^4\left(x^2-1\right)-9x^2\left(x-1\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)
\(=\left(x-1\right)\left[x^4\left(x+1\right)-9x^2\right]\)
\(=\left(x-1\right)\left(x^5+x^4-9x^2\right)\)
a/ \(x^4+2x^3-4x-4\)
\(=x^4-2x^2+2x^3-4x+2x^2-4\)
\(=x^2\left(x^2-2\right)+2x\left(x^2-2\right)+2\left(x^2-2\right)\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
b/ \(x^3-19x-30\)
\(=x^3+2x^2-2x^2-4x-15x-30\)
\(=x^2\left(x+2\right)-2x\left(x+2\right)-15\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-2x-15\right)\)
\(=\left(x+2\right)\left(x+3\right)\left(x-5\right)\)
c/ \(x^3-7x-6\)
\(=x^3+x^2-x^2-x-6x-6\)
\(=x^2\left(x+1\right)-x\left(x+1\right)-6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x-6\right)\)
\(=\left(x+1\right)\left(x+2\right)\left(x-3\right)\)