Polynomial Solver Step by Step
ASO Keyword Dashboard
Tracking 40 keywords for Polynomial Solver Step by Step in Apple App Store
Polynomial Solver Step by Step tracks 40 keywords (no keywords rank yet; 40 need traction). Key metrics: opportunity 70.2, difficulty 40.2.
Tracked keywords
40
0 ranked • 40 not ranking yet
Top 10 coverage
—
Best rank — • Latest leader —
Avg opportunity
70.2
Top keyword: method
Avg difficulty
40.2
Lower scores indicate easier wins
Opportunity leaders
- 64.7
method
Opportunity: 73.0 • Difficulty: 39.0 • Rank —
Competitors: 41
- 63.8
outside
Opportunity: 73.0 • Difficulty: 38.7 • Rank —
Competitors: 71
- 67.8
solving
Opportunity: 73.0 • Difficulty: 41.1 • Rank —
Competitors: 188
- 63.9
teaching
Opportunity: 73.0 • Difficulty: 38.6 • Rank —
Competitors: 24
- 67.9
known
Opportunity: 73.0 • Difficulty: 41.1 • Rank —
Competitors: 99
Unranked opportunities
method
Opportunity: 73.0 • Difficulty: 39.0 • Competitors: 41
outside
Opportunity: 73.0 • Difficulty: 38.7 • Competitors: 71
solving
Opportunity: 73.0 • Difficulty: 41.1 • Competitors: 188
teaching
Opportunity: 73.0 • Difficulty: 38.6 • Competitors: 24
known
Opportunity: 73.0 • Difficulty: 41.1 • Competitors: 99
High competition keywords
help
Total apps: 149,163 • Major competitors: 1,295
Latest rank: — • Difficulty: 52.4
like
Total apps: 142,323 • Major competitors: 1,824
Latest rank: — • Difficulty: 52.3
features
Total apps: 115,265 • Major competitors: 1,119
Latest rank: — • Difficulty: 51.3
available
Total apps: 88,778 • Major competitors: 1,008
Latest rank: — • Difficulty: 50.5
real
Total apps: 84,329 • Major competitors: 964
Latest rank: — • Difficulty: 50.1
All tracked keywords
Includes opportunity, difficulty, rankings and competitor benchmarks
| Major Competitors | |||||||
|---|---|---|---|---|---|---|---|
| online | 68 | 100 | 49 | 81 67,390 competing apps Median installs: 50 Avg rating: 4.1 | — | — | 719 major competitor apps |
| level | 68 | 100 | 48 | 79 51,352 competing apps Median installs: 75 Avg rating: 4.2 | — | — | 674 major competitor apps |
| step | 69 | 100 | 46 | 76 36,869 competing apps Median installs: 50 Avg rating: 4.2 | — | — | 326 major competitor apps |
| welcome | 69 | 100 | 47 | 78 45,053 competing apps Median installs: 50 Avg rating: 4.3 | — | — | 365 major competitor apps |
| available | 67 | 100 | 50 | 83 88,778 competing apps Median installs: 50 Avg rating: 4.1 | — | — | 1,008 major competitor apps |
| basic | 72 | 100 | 43 | 71 17,490 competing apps Median installs: 50 Avg rating: 4.1 | — | — | 88 major competitor apps |
| help | 65 | 100 | 52 | 87 149,163 competing apps Median installs: 50 Avg rating: 4.2 | — | — | 1,295 major competitor apps |
| write | 72 | 100 | 42 | 70 15,451 competing apps Median installs: 75 Avg rating: 4.1 | — | — | 102 major competitor apps |
| real | 67 | 100 | 50 | 82 84,329 competing apps Median installs: 50 Avg rating: 4.1 | — | — | 964 major competitor apps |
| like | 65 | 100 | 52 | 86 142,323 competing apps Median installs: 75 Avg rating: 4.2 | — | — | 1,824 major competitor apps |
| advanced | 69 | 100 | 47 | 78 47,539 competing apps Median installs: 50 Avg rating: 4.2 | — | — | 373 major competitor apps |
| companion | 71 | 100 | 44 | 73 23,681 competing apps Median installs: 25 Avg rating: 4.2 | — | — | 90 major competitor apps |
| qr | 72 | 100 | 42 | 70 14,313 competing apps Median installs: 25 Avg rating: 4.1 | — | — | 90 major competitor apps |
| calculation | 72 | 100 | 37 | 61 4,591 competing apps Median installs: 25 Avg rating: 4.1 | — | — | 17 major competitor apps |
| adjustable | 72 | 100 | 37 | 61 4,590 competing apps Median installs: 100 Avg rating: 4.1 | — | — | 37 major competitor apps |
| possible | 71 | 100 | 44 | 72 20,686 competing apps Median installs: 50 Avg rating: 4.1 | — | — | 131 major competitor apps |
| features | 66 | 100 | 51 | 85 115,265 competing apps Median installs: 50 Avg rating: 4.1 | — | — | 1,119 major competitor apps |
| long | 70 | 100 | 45 | 75 29,851 competing apps Median installs: 75 Avg rating: 4.2 | — | — | 258 major competitor apps |
| global | 71 | 100 | 45 | 73 23,685 competing apps Median installs: 50 Avg rating: 4.3 | — | — | 265 major competitor apps |
| starting | 72 | 100 | 42 | 69 13,159 competing apps Median installs: 50 Avg rating: 4.3 | — | — | 140 major competitor apps |
| algorithm | 72 | 100 | 37 | 61 4,290 competing apps Median installs: 75 Avg rating: 4.2 | — | — | 26 major competitor apps |
| method | 73 | 100 | 39 | 65 7,298 competing apps Median installs: 50 Avg rating: 4.1 | — | — | 41 major competitor apps |
| complex | 72 | 100 | 42 | 70 14,968 competing apps Median installs: 50 Avg rating: 4.2 | — | — | 76 major competitor apps |
| interactive | 69 | 100 | 46 | 77 40,088 competing apps Median installs: 50 Avg rating: 4.2 | — | — | 234 major competitor apps |
| outside | 73 | 100 | 39 | 64 6,440 competing apps Median installs: 50 Avg rating: 4.1 | — | — | 71 major competitor apps |
App Description
It is designed to help students of both basic and advanced levels.
Basic Algebra functions:
1. Polynomial multiplication.
2. Polynomial long division with step by step explanation.
3. Algorithm for finding rational roots consisting of the following:
a. Finding all possible rational roots.
b. Eliminating the roots outside bounds.
c. Performing polynomial long division for each of the roots.
d. Adjusting bounds based on long division results if appropriate.
Iterative polynomial solving algorithms for advanced-level students:
1. Durand-Kerner method.
2. Aberth method.
3. Newton method with both real and complex starting points.
4. Global (also known as "damped") Newton method with both real and complex starting points.
5. Laguerre method with both real and complex starting points.
6. Bairstow method.
7. Muller method.
8. Eigenvalues of ‘companion matrix’ (demonstration of QR algorithm for eigenvalue calculation is available in our “Matrix Solver Step by Step" app).
Interactive graphs are available for:
1. Polynomial functions and their derivatives.
2. Aberth and Durand-Kerner method points on complex plane.
3. Newton, global Newton, Laguerre, and Muller algorithm steps.
4. Newton and global Newton method fractals / convergence images on complex plane
5. Laguerre method convergence images on complex plane
6 Bairstow method convergence images depending on initial approximation values.
7 Muller method convergence images depending on initial approximation values.
(Images 4-7 have adjustable settings for area, resolution and shading).
Links to online references are included.
Please write to us if you like to have new features / chapters added!
Developers welcome any feedback, please write to us at graphmath@aol.com.