WiSku$de I oeËeningen DEEI.,J
Veeltermen
2.2.1,.1. (o"t. ""-/^A ?r'(
1)
(-3x2)(5x3)
(-3) * 5*tcz *tc3
-LS xs
2)
(6x2 -3x + 5) - (2x' + 6x
- 9)
6xz - 3r + 5 -zxz -5x *9
Bxz -Bx *L4
3)
-Zx(x+5X3r-2)
(-2x'- 10r)(3x - 2)
(-6x3 + 4x2) * (-30x2 * 20x)
-6x3 -26x2 +Zox
4)
(4x' -7x -2) - x(Zx + 3) - (2x * 5)(x - 2)
4xz -7x -2-Zxz +3x - (2xz - 4x* 5r - 10)
Axz -7x -2-Zxz +3x-Zxz * 4x - 5x * 10
4xz -2x2 -zxz -7x +3x * 4x - 5x * 1o - 2
-5r*B
s)
((x -x2.,-r)) - (x2)- ((*'-3x *2x- 6) - x +7) + (1- 2x + 4xz))
-x2 + 2x - x2 - x2 + x r 6 * x - 7 - L r 2x - 4x2
-7x2 +6x-2
ÊtË€Ê * vós ên dnor 8te'rdÊ.|á€f*
4P es.rsa lstr,nàrdt 7
?Fgrs.anaen*P.
, 6)
(-4x')' + Z x (-Axr)(-gx2) + (-3xz)z
'l.6xta +24xe +gx4
7)
(7xz)z + (-3x)2 + (-z)2 + 2(Txz)(-3x) + 2(-3 x)(-2) + 2(7xz)(_Z)
49x4 + 9x2 + 4 - 42x3 * L2x - 2\xz
49xa-42x3-Lgxz+12x*4
B)
(3x3 - 2261t
(3xt)t + 3(313)2(-2x) + 3(3x3)(-2x)z + (-2x)Z
27xe -54x7 +36xs - gx3
e)
(3x+2)(9x2-6x++)
27x3 -78x2 +L2x*LBxz -I2xrB
10)
3x2 +
"lE* €x - ffi * rllx6 - 13
3xz +,lT6x - tlídx - L3
3x2 - rg
2.2.L.2 J.t1^ rX 2Á
1)
|-,r xz(x + t\
x(x + L)2 x3
(x + 7)(x + I1z ' (x+L)z(x+t)'
FTF
x(xz+2x+t)+13+ x2+x3
(r + 1)3
x3 +zxz *x*x3 +x2 +x3
(x+
3x3 +3x2 + x
(r + 1)3
díscrímtnant ís negatief dus we kunnenniet opd.elen
ï(/ORD ;t,i ttf*XnffiHï ', rili ltllili
KËïJT? 2
, 2l
opgelet opgave kan anders geschreven worden
141 3(r+1)
\x+il-@
4(x+2)-3(r+ 1)
+
4x*B-3r-3
(x +2)2
r+5
(x + 2)z
3)
x2 +x* 1 = (. *ï)' *ï:, niet bruíkbaar
x3-L=(x2*x+L)(x-L)
x(xz + x * L)2 + (x - L)(x +1) - (rt * x2 - 3)(x2+x+L)
(r+1) *r*1)
(xka +x2 +L+Zxs +2x *zxz) + x2 +1- (rs +x4 + xs + xa+13 + x2 -3xz - 3x-3))
(x*L)(xz*x*7)2
x(xa + 2xs + Bx2 + 2x + l) + x2 + I - (xs + zx4 * 2x3 - zxz -3r - 3)
(x +7)(xztx*1)z
(xs + zx4 * 3xs * zxz *x* x2 * 1- xs - Zxa - zx3 + zxz + zx + 3)
(x + 1)(x2 * x *L)z
x3+sxzzx+4
(x+l)(x2*x*L)2
2.2.2.3
1)
6x3 -7x2 -7x 7 2x+7
6x3 3x2
0 -10x2
-10x2 -5x
-2x t
-2x -1
0
3
Keps & Promeco
,2)
18x3 0+x -5 3x-2
18x3 72xz 5x2+4x+3
t2x2 +x
L2xz -8x
9x -5
9x +6
t
1Bx3 +r - 5 = (3x -1) ,r(6x^24x+3)+I/(3x -Z)
x (6x^2 4x + 3) + L/(3x - 2)
3)
12x^5 -2x^4 0 -19x2 0 9 6x2-x-3
12x^5 -2x^4 -6x3 2x3+x-3
6x3 -19x2 0
5x3 -xz -3x
-18x2 -3x I
-18x2 -3x 9
0
4l
3x^4 -7xt -x2 1ox -3 x2-3x+2
2x-
3x^4 -9x3 +6x2 1
2xs -7x2 L0x
2x3 -6x2 4x
_x2 6x -3
_x2 3x -2
4
Keps & Promeco
, 3x 7
2.2.2.5
1)
x2 5x 4
-4 -4 -4
1 L 0
L L
L 0
-(r+Q@+1Xx+1)x1
2l
_x3 0 -4x L5
2 -2 -4 -15
-t -z -8 0
-- (-*, - Zx - qlc - Z)
3)
2x^4 0 0 7 -1
-1 -2 2 -2 L
2 -2 2 -L 0
- (x + L)(2x3 -Zxz +2x -L)
4)
x3 4xz 5x 6
-3 -3 -3 -6
t t 2
- (x*3)(x2 +xrZ)
5
Keps & Promeco
, 6l/
2,2.9.6
Ontbind in factoren:
L)
4x2 x -18
2 8 L8
4 9 0
(x-2Xax+9)
2l
3(x3+a)
L 0 0 I
-2 -2 4 -8
t -2 4 0
3(x+2)(x2-2x+4)
3)
2 L-5 2
L 2 3 -2
2 3 -2 0
-2 -4 2
2 -L 0
(x-1)(x2+3x-2)
(x-1Xx+2X2x-1)
4l
2 -6 6-Z
L 2 -4 2
2 -4 z 0
6
Keps & Promeco
Veeltermen
2.2.1,.1. (o"t. ""-/^A ?r'(
1)
(-3x2)(5x3)
(-3) * 5*tcz *tc3
-LS xs
2)
(6x2 -3x + 5) - (2x' + 6x
- 9)
6xz - 3r + 5 -zxz -5x *9
Bxz -Bx *L4
3)
-Zx(x+5X3r-2)
(-2x'- 10r)(3x - 2)
(-6x3 + 4x2) * (-30x2 * 20x)
-6x3 -26x2 +Zox
4)
(4x' -7x -2) - x(Zx + 3) - (2x * 5)(x - 2)
4xz -7x -2-Zxz +3x - (2xz - 4x* 5r - 10)
Axz -7x -2-Zxz +3x-Zxz * 4x - 5x * 10
4xz -2x2 -zxz -7x +3x * 4x - 5x * 1o - 2
-5r*B
s)
((x -x2.,-r)) - (x2)- ((*'-3x *2x- 6) - x +7) + (1- 2x + 4xz))
-x2 + 2x - x2 - x2 + x r 6 * x - 7 - L r 2x - 4x2
-7x2 +6x-2
ÊtË€Ê * vós ên dnor 8te'rdÊ.|á€f*
4P es.rsa lstr,nàrdt 7
?Fgrs.anaen*P.
, 6)
(-4x')' + Z x (-Axr)(-gx2) + (-3xz)z
'l.6xta +24xe +gx4
7)
(7xz)z + (-3x)2 + (-z)2 + 2(Txz)(-3x) + 2(-3 x)(-2) + 2(7xz)(_Z)
49x4 + 9x2 + 4 - 42x3 * L2x - 2\xz
49xa-42x3-Lgxz+12x*4
B)
(3x3 - 2261t
(3xt)t + 3(313)2(-2x) + 3(3x3)(-2x)z + (-2x)Z
27xe -54x7 +36xs - gx3
e)
(3x+2)(9x2-6x++)
27x3 -78x2 +L2x*LBxz -I2xrB
10)
3x2 +
"lE* €x - ffi * rllx6 - 13
3xz +,lT6x - tlídx - L3
3x2 - rg
2.2.L.2 J.t1^ rX 2Á
1)
|-,r xz(x + t\
x(x + L)2 x3
(x + 7)(x + I1z ' (x+L)z(x+t)'
FTF
x(xz+2x+t)+13+ x2+x3
(r + 1)3
x3 +zxz *x*x3 +x2 +x3
(x+
3x3 +3x2 + x
(r + 1)3
díscrímtnant ís negatief dus we kunnenniet opd.elen
ï(/ORD ;t,i ttf*XnffiHï ', rili ltllili
KËïJT? 2
, 2l
opgelet opgave kan anders geschreven worden
141 3(r+1)
\x+il-@
4(x+2)-3(r+ 1)
+
4x*B-3r-3
(x +2)2
r+5
(x + 2)z
3)
x2 +x* 1 = (. *ï)' *ï:, niet bruíkbaar
x3-L=(x2*x+L)(x-L)
x(xz + x * L)2 + (x - L)(x +1) - (rt * x2 - 3)(x2+x+L)
(r+1) *r*1)
(xka +x2 +L+Zxs +2x *zxz) + x2 +1- (rs +x4 + xs + xa+13 + x2 -3xz - 3x-3))
(x*L)(xz*x*7)2
x(xa + 2xs + Bx2 + 2x + l) + x2 + I - (xs + zx4 * 2x3 - zxz -3r - 3)
(x +7)(xztx*1)z
(xs + zx4 * 3xs * zxz *x* x2 * 1- xs - Zxa - zx3 + zxz + zx + 3)
(x + 1)(x2 * x *L)z
x3+sxzzx+4
(x+l)(x2*x*L)2
2.2.2.3
1)
6x3 -7x2 -7x 7 2x+7
6x3 3x2
0 -10x2
-10x2 -5x
-2x t
-2x -1
0
3
Keps & Promeco
,2)
18x3 0+x -5 3x-2
18x3 72xz 5x2+4x+3
t2x2 +x
L2xz -8x
9x -5
9x +6
t
1Bx3 +r - 5 = (3x -1) ,r(6x^24x+3)+I/(3x -Z)
x (6x^2 4x + 3) + L/(3x - 2)
3)
12x^5 -2x^4 0 -19x2 0 9 6x2-x-3
12x^5 -2x^4 -6x3 2x3+x-3
6x3 -19x2 0
5x3 -xz -3x
-18x2 -3x I
-18x2 -3x 9
0
4l
3x^4 -7xt -x2 1ox -3 x2-3x+2
2x-
3x^4 -9x3 +6x2 1
2xs -7x2 L0x
2x3 -6x2 4x
_x2 6x -3
_x2 3x -2
4
Keps & Promeco
, 3x 7
2.2.2.5
1)
x2 5x 4
-4 -4 -4
1 L 0
L L
L 0
-(r+Q@+1Xx+1)x1
2l
_x3 0 -4x L5
2 -2 -4 -15
-t -z -8 0
-- (-*, - Zx - qlc - Z)
3)
2x^4 0 0 7 -1
-1 -2 2 -2 L
2 -2 2 -L 0
- (x + L)(2x3 -Zxz +2x -L)
4)
x3 4xz 5x 6
-3 -3 -3 -6
t t 2
- (x*3)(x2 +xrZ)
5
Keps & Promeco
, 6l/
2,2.9.6
Ontbind in factoren:
L)
4x2 x -18
2 8 L8
4 9 0
(x-2Xax+9)
2l
3(x3+a)
L 0 0 I
-2 -2 4 -8
t -2 4 0
3(x+2)(x2-2x+4)
3)
2 L-5 2
L 2 3 -2
2 3 -2 0
-2 -4 2
2 -L 0
(x-1)(x2+3x-2)
(x-1Xx+2X2x-1)
4l
2 -6 6-Z
L 2 -4 2
2 -4 z 0
6
Keps & Promeco
