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Excalidraw Data
Text Elements
3x^3-15x^2-36
3x^2-6x-18
(x-3)
3x^3-9x^2
-6x^2
-36
-6x^2-18x
-18x-36
-18x-54
18
2
4
7
0
-3
4
8
15
30
30
60
57
remainder
constant
x
x^2
4x^2+15x+30+(57/(x-2))
4
15
-124
-4
4
-16
-1
4
-120
4x^2-15x-124)/(x-4)
-4x^4+0x^3-6x^2-7x+6
+2
-4
0
-6
-7
6
-4
-8
-8
-16
-22
-44
-51
-102
96
(6-7x-6x^2-4x^4)/(x+2)
x+3
1
0
0
0
0
243
1
3
3
9
9
27
27
81
81
243
486
x^4+3x^3+9x^2+27x+(486/x+3)+81
x^4-3x^3+9x^2-27x+81
2x^3-x^2-10x+5
2
-1
-10
5
1
2
2
1
1
-9
-9
-4
2x^3+3x+13 R18
2
-1
-10
5
.5
2
1
0
0
-10
-5
0
2x^3+3x+13 R18
2
-1
-10
5
sqrt(5)
2
2sqrt(5)
2x^3+3x+13 R18
2sqrt(5)-1
sqrt(5)(-1)+10
sqrt(5)(-1)
-5
0
2
-1
-10
5
-1
2
-2
2x^3+3x+13 R18
-3
3
-7
7
13
1
-4
-2
8
-sqrt(2)
1
-sqrt(2)
-4-sqrt(2)
4sqrt(2)
-8
0
1
-4
-2
8
-3
1
-3
-7
19
-57
-49
21
4 25 -8 -84
-2
4
-8
17
-34
84
-42
0
(x+2)(4x^2+17x-42)
(x+2)(4x-7)(x+6)
1/4
20 103 13 -10
20
5
108
27
40
10
0
(20x^2+108x+40)(x-1/4) 4(5x^2+27x+10)(x+2)
(5x+2)(x+5)(4x-1)
(x+2sqrt(13))(x-2sqrt(13)) x^2-2(sqrt13)x+2(sqrt(13)x+2sqrt(13)-2sqrt(13) x^2+(2sqrt13-2sqrt13) x^2-2sqrt(13)^2 x^2-52
-5, 2i, -2i
(x+5)(x-2i)(x+2i) x^3+5x^2+4x+20
-3i*3i -9-3i+3i+i^2 -9-1 -8
(sqrt(3)-sqrt(12)i)(sqrt(3)+sqrt(12)i) sqrt(3)*sqrt(3) 3 sqrt(3)*sqrt(12)i 6i -sqrt(12i)*sqrt(3) -6i -sqrt(12i)*sqrt(12) -12i
3+6i-6i-12i
3*-12=-36
fundamental theorum of algebra: if a polynomial has a degree higher than 1 with complex coefficients, then f(x) has atleast one complex zero
x^4-10x^3+72x^2+20x-148
5-7i 5+7i
(x^2-2)(x^2-10x+74)
(x-(5-7i))(x-(5+7i))(x-sqrt(2))(x+sqrt(2))
5x^3-53x^2+160x-78
2x^5+9x^4+9x^3+7x^2-47x+20
(x-1)(2x-1)(x+4)(x^2+2x+5)
-5i +5i 6/5
(x+5i)(x-5i)(x-6/5) (x^2-(5i)^2)(x-6/5) (x^2-25i^2)(x-6/5) (x^2+25)(x-6/5) x^3-6/5x^2+25x-30 5x^3-6x+125x-150
zeros: -4 ( multiplicity 3 ) 1 ( multiplicity 1 ) 320 ( multiplicity 1 )
(x+4)^3(x-1)(x-320) (x^3+4^3)(x-1)(x-320) (x^3+4^3)(x^2-320x-x+320) (x^3+4^3)(x^2-321x+320) (x^3+64)(x^2-321x+320)
−5(x+4)3(x−1)
-15x^2-45x+60
-5x^{4}-55x^{3}-180x^{2}-80x+320
x^3-5x^2+12x+18
-1 3-3i 3+3i
(x-7i)(x+7i)(x-4/5) (x-7i)^2(x-4/5) (x^2-14ix-49)(x-4/5) x^3-4/5x^2-14ix^2+(4/5)(14ix)-49x-(49)(4/5)
5x^3-4x^2-70ix^2+56ix-245x-196)
(x^2+49)(x-4/5) x^3-4/5x^2+49x-(4/5)49 5x^3-4x^2+245x-196
4
1
0
0
0
0
-1024
1
4
4
16
16
64
64
256
256
1024
0
3x^4-7x^3-7x^2+42x-19 3(3)^4-7(3)^3-7(3)^2+42(3)-19 98
-2x^6(x+7)^2(x-5)^2
2x^5+19x^4+75x^3+90x^2-162x-324
2
19
75
90
-162
-324
-3/2
2
-3
16
-24
51
-76.5
13.5
-20.25
-36.25
54.375
-269.625
(-3-3i)(-3+3i) (-3^2-3i^2) (-9-3) (-6)
((3)^3+6(3))^3+6((3)^3+6(3))
4x^3-17x^2-x+29
x-4
4x^3+8x^2
4x^2+9x+35
9x^2
-9x^2+36x
35x
-35x+140
169
9