Stockholms Tekniska Gymnasium 2013-03-19
Övningsblad i faktorisering Faktorisera så långt som möjligt/bryt ut största möjliga faktor
= x + x3
2 2 __________________________
=
4x+ 8 __________________________
=
+ 3
4 11
3a a __________________________
=
5x2 + 25 __________________________
= + 2
2 3
33x y __________________________
=
+ 2
2 11
7y y __________________________
=
14y2 +12 __________________________
=
3x2 − 9 __________________________
=
− 2
2 10
5x y __________________________
=
− 2
2 7
4y y __________________________
=
5y2 −15 __________________________
= x + x6
2 2 __________________________
= x + x8
4 3 __________________________
= + a b b
a4 2 11 3
3 __________________________
= + 9
2 7
35x x __________________________
= + 3
2 3
9x x __________________________
= + 3 2
2 11
7xy x y __________________________
= + 11
8 2
6y y __________________________
=
− 3
2 6
12x x __________________________
=
− 3 4
2 11
7x y x y __________________________
=
− 6
4 7
49y y __________________________
=
− + 7 11 5 9
8
9 12 4
6x y x y x y __________________________
=
−
− 3 8 4 4
9
4 33 44
11x y x y x y __________________________
=
−
+ 9 4 5 9
6
2 13 23
3x y x y x y __________________________
=
−
− 7 7 5 5
9
9 4 6
2x y x y x y __________________________
Stockholms Tekniska Gymnasium 2013-03-19
= + 4
2 8
2x x __________________________
=
8x+ 2 __________________________
=
+ 3
2 11a
a __________________________
=
9x2 − 3 __________________________
=
− 3
2 30
10x x __________________________
=
− 3
2 32
16y y __________________________
= + 2 3
2 8
2xy x y __________________________
=
− 6
4 18
6y y __________________________
=
−
− 7 7 9 9
5
5 4 6
2x y x y x y __________________________
=
−
− 3 4 5
2
6 4 8
16x y x y x y __________________________
=
2 −1
x __________________________
=
− 2
9 x __________________________
=
4a2 − 36 __________________________
=
9x2 −16 __________________________
=
2 − 25
2y
x __________________________
=
2x2 −18 __________________________
=
−3 2
75 x __________________________
= + +4 4
2 x
x __________________________
= + +6 9
2 y
y __________________________
= +
+ 2
2 2xy y
x __________________________
= + +16 64
2 x
x __________________________
= + +16 16
4x2 x __________________________
= +
−4 4
2 x
x __________________________
= +
−6 9
2 y
y __________________________
= +
− 2
2 2xy y
x __________________________
= +
−16 64
2 x
x __________________________
= +
−16 16
4x2 x __________________________
Stockholms Tekniska Gymnasium 2013-03-19
Facit )
3 2 ( 3 2
3
2x2 + x= x⋅ x+x⋅ =x x+ )
2 ( 4 8
4x+ = x+
) 11 3 ( 11
3a4 + a3 =a3 a+ ) 5 ( 5 25
5x2 + = x2 +
) 11
( 3 3
33x2 + y2 = x2 + y2
2 2
2
2 11 (7 11) 18
7y + y = y + = y )
6 7 ( 2 12
14y2 + = y2 +
) 3 ( 3 9
3x2 − = x2 −
) 2 ( 5 10
5x2 − y2 = x2 − y2
2 2
2
2 7 (4 7) 3
4y − y = y − =− y )
3 ( 5 15
5y2 − = y2 −
) 3 ( 2 6
2x2 + x = x x+ ) 2 ( 4 8
4x3 + x= x x2 +
) 11 3
( 11
3a b + a b = a4 2 3 3b ab+ 35x2 + 7x9 = 7x2 (5 + x7 ) 9x2 + 3x3 = 3x2 (3 + x) 7xy2 +11x3 y2 = xy2 (7 +11x2) 6y8 + 2y11 = 2y8 (3 + y3 )
12x2− 6x3= 6x2(2 − x)
7x2y −11x3y4= x2y(7 −11xy3) 49y4− 7 y6= 7 y4(7 − y2)
6x9 y8 +12x7 y11 − 4x5 y9 = 2x5 y8 (3x4 + 6x2 y3 − 2y) 11x4 y9 − 33x3 y8 − 44x4 y4 = 11x3 y4 (xy5 − 3y4 − 4x) 3x2 y6 +13x9 y4 − 23x5 y9 = x2 y4 (3y2 +13x7 − 23x3 y5 ) 2x9 y9 − 4x7 y7 − 6x5 y5 = 2x5 y5 (x4 y4 − 2x2 y2 − 3)
Stockholms Tekniska Gymnasium 2013-03-19
) 4 1 ( 2 8
2x2 + x4 = x2 + x2 )
1 4 ( 2 2
8x+ = x+ ) 11 1 ( 11 3 2
2 a a a
a + = +
) 1 3 ( 3 3
9x2 − = x2 − ) 3 1 ( 10 30
10x2 − x3 = x2 − x ) 2 1 ( 16 32
16y2 − y3 = y2 − y ) 4 1 ( 2 8
2xy2 + x2y3 = xy2 + xy ) 3 1 ( 6 18
6y4 − y6 = y4 − y2
) 3 2
1 ( 2 6
4
2x5y5 − x7y7 − x9y9 = x5y5 − x2y2 − x4y4 ) 2 1 4
( 4 8
4
16x6y2 − x3y− x4y5 = x3y x3y− − xy4
) 1 )(
1 (
2 1
− +
=
− x x
x
) 3 )(
3 (
9−x2 = +x −x ) 6 2 )(
6 2 ( 36
4a2 − = a+ a− ) 4 3 )(
4 3 ( 16
9x2 − = x+ x− ) 5 )(
5 (
2 25
2y − = xy+ xy−
x
) 3 )(
3 ( 2 ) 9 ( 2 18
2x2 − = x2 − = x+ x− ) 5 )(
5 ( 3 ) 25 ( 3 3
75− x2 = −x2 = +x −x
2 2 +4x+4=(x+2) x
2 2 +6y+9=(y+3) y
2 2
2 2xy y (x y)
x + + = +
2 2 +16x+64=(x+8) x
2 2
2 16 16 4( 4 4) 4( 2)
4x + x+ = x + x+ = x+
2 2 −4x+4=(x−2) x
2 2 −6y+9=(y−3) y
2 2
2 2xy y (x y)
x − + = −
2 2 −16x+64=(x−8) x
2 2
2 16 16 4( 4 4) 4( 2)
4x − x+ = x − x+ = x−
