Polynomial Solver Step by Step
ASO Keyword Dashboard
Tracking 42 keywords for Polynomial Solver Step by Step in Apple App Store
Polynomial Solver Step by Step tracks 42 keywords (3 keywords rank; 39 need traction). Key metrics: 0% top-10 coverage, opportunity 70.3, difficulty 41.6, best rank 70.
Tracked keywords
42
3 ranked • 39 not ranking yet
Top 10 coverage
0%
Best rank 70 • Latest leader —
Avg opportunity
70.3
Top keyword: method
Avg difficulty
41.6
Lower scores indicate easier wins
Opportunity leaders
- 64.9
method
Opportunity: 73.0 • Difficulty: 40.0 • Rank —
Competitors: 80
- 63.8
outside
Opportunity: 73.0 • Difficulty: 40.3 • Rank —
Competitors: 134
- 67.8
solving
Opportunity: 73.0 • Difficulty: 43.1 • Rank —
Competitors: 307
- 64.0
teaching
Opportunity: 73.0 • Difficulty: 40.1 • Rank —
Competitors: 50
- 67.8
known
Opportunity: 73.0 • Difficulty: 43.1 • Rank —
Competitors: 193
Unranked opportunities
method
Opportunity: 73.0 • Difficulty: 40.0 • Competitors: 80
outside
Opportunity: 73.0 • Difficulty: 40.3 • Competitors: 134
solving
Opportunity: 73.0 • Difficulty: 43.1 • Competitors: 307
teaching
Opportunity: 73.0 • Difficulty: 40.1 • Competitors: 50
known
Opportunity: 73.0 • Difficulty: 43.1 • Competitors: 193
High competition keywords
help
Total apps: 162,218 • Major competitors: 2,474
Latest rank: — • Difficulty: 54.9
like
Total apps: 153,372 • Major competitors: 3,285
Latest rank: — • Difficulty: 55.4
features
Total apps: 126,019 • Major competitors: 2,127
Latest rank: — • Difficulty: 53.9
real
Total apps: 105,223 • Major competitors: 1,803
Latest rank: — • Difficulty: 53.7
available
Total apps: 95,740 • Major competitors: 1,851
Latest rank: — • Difficulty: 54.5
All tracked keywords
Includes opportunity, difficulty, rankings and competitor benchmarks
| Major Competitors | |||||||
|---|---|---|---|---|---|---|---|
| explanations | 72 | 100 | 36 | 60 3,838 competing apps Median installs: 450 Avg rating: 4.3 | 70 | 70 | 24 major competitor apps |
| explanation | 71 | 100 | 33 | 55 2,048 competing apps Median installs: 350 Avg rating: 4.0 | 146 | 96 | 12 major competitor apps |
| algorithm | 72 | 100 | 38 | 61 4,697 competing apps Median installs: 550 Avg rating: 4.1 | 155 | 155 | 54 major competitor apps |
| online | 68 | 100 | 52 | 81 73,698 competing apps Median installs: 550 Avg rating: 4.1 | — | — | 1,306 major competitor apps |
| level | 68 | 100 | 50 | 79 55,864 competing apps Median installs: 550 Avg rating: 4.1 | — | — | 1,185 major competitor apps |
| step | 69 | 100 | 48 | 77 42,112 competing apps Median installs: 500 Avg rating: 4.1 | — | — | 644 major competitor apps |
| welcome | 69 | 100 | 49 | 78 50,061 competing apps Median installs: 350 Avg rating: 4.2 | — | — | 689 major competitor apps |
| available | 67 | 100 | 54 | 83 95,740 competing apps Median installs: 550 Avg rating: 4.1 | — | — | 1,851 major competitor apps |
| basic | 72 | 100 | 44 | 71 18,966 competing apps Median installs: 400 Avg rating: 4.0 | — | — | 194 major competitor apps |
| help | 65 | 100 | 55 | 87 162,218 competing apps Median installs: 450 Avg rating: 4.1 | — | — | 2,474 major competitor apps |
| write | 72 | 100 | 44 | 70 16,684 competing apps Median installs: 500 Avg rating: 4.0 | — | — | 213 major competitor apps |
| real | 67 | 100 | 54 | 83 105,223 competing apps Median installs: 550 Avg rating: 4.0 | — | — | 1,803 major competitor apps |
| like | 66 | 100 | 55 | 86 153,372 competing apps Median installs: 600 Avg rating: 4.1 | — | — | 3,285 major competitor apps |
| advanced | 69 | 100 | 49 | 79 54,163 competing apps Median installs: 500 Avg rating: 4.1 | — | — | 760 major competitor apps |
| companion | 70 | 100 | 45 | 74 27,813 competing apps Median installs: 350 Avg rating: 4.1 | — | — | 182 major competitor apps |
| qr | 72 | 100 | 45 | 70 16,415 competing apps Median installs: 350 Avg rating: 4.0 | — | — | 169 major competitor apps |
| calculation | 72 | 100 | 38 | 62 5,171 competing apps Median installs: 300 Avg rating: 4.0 | — | — | 31 major competitor apps |
| adjustable | 72 | 100 | 39 | 62 5,270 competing apps Median installs: 744 Avg rating: 4.0 | — | — | 67 major competitor apps |
| possible | 71 | 100 | 45 | 72 21,915 competing apps Median installs: 400 Avg rating: 4.0 | — | — | 274 major competitor apps |
| features | 66 | 100 | 54 | 85 126,019 competing apps Median installs: 550 Avg rating: 4.1 | — | — | 2,127 major competitor apps |
| long | 70 | 100 | 48 | 75 34,098 competing apps Median installs: 548 Avg rating: 4.1 | — | — | 522 major competitor apps |
| global | 71 | 100 | 49 | 74 26,667 competing apps Median installs: 600 Avg rating: 4.1 | — | — | 510 major competitor apps |
| starting | 72 | 100 | 43 | 69 14,562 competing apps Median installs: 500 Avg rating: 4.2 | — | — | 254 major competitor apps |
| method | 73 | 100 | 40 | 65 8,010 competing apps Median installs: 400 Avg rating: 4.0 | — | — | 80 major competitor apps |
| complex | 72 | 100 | 44 | 70 17,216 competing apps Median installs: 450 Avg rating: 4.1 | — | — | 159 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.