Escape from Pixel Castle
Start
Introduction
While you are traveling through unexplored areas of China, you have been captured by the soldiers of the Pixel King's Castle. You will need to gather courage and overcome the trials that the King will put you through in order to try to obtain the pixel coins, pay for your release with them, and continue your journey.
Let's go!
select mission
PIXEl rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Fake doors
You must correctly answer the various questions to find the only true door and advance in your mission.
Start
WHAT TYPE OF SOLUTION WOULD THE FOLLOWING HAVE:
INFINITE SOLUTION
REAL NUMBERS
COMPLEX NUMBERS
1/3
Great!
You chose the correct door
Next
1/3
What is the general form when factoring over the complex numbers?
(a+b)(a-b)
(a+bi)(a-bi)
(a+b)2
2/3
Take it!
You chose the correct door
Next
2/3
When using the Sum of Squares Pattern, how do we find "a" and "b"?
Take the Square Root of a2 and b2
Divide by "a" and "b"
Complete the Square
3/3
Well done!
You have a pixel coin! Three more will be enough to buy your freedom
Continues
3/3
ERROR!
Ouch! What a headache.Try again.
Return
ERROR!
Ouch! What a headache.Try again.
Return
Error!
Ouch! What a headache.Try again.
Return
MISSION MAPS
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Maths jump
Solve math calculation problems to advance in this mission. Jump on the correct answer and demonstrate your skills.
Start
Easy one first!What are the factors of:
A. (x+6)2
B. (x+6)(x-6)
C. (x+6i)(x-6i)
D. (x-6i)2
1/4
Well done!
You have jumped to the correct answer
Next
1/4
What are the factors of?
A. (3x+5)(3x-5)
B. (3x+5i)(3x-5i)
C. (3x+5i)2
D. (5x+3i)(5x-3i)
2/4
Yeah!
You have jumped on the correct answer
Next
2/4
In the following example, what must you do first in order to factor over the complex numbers?
A. FACTOR OUT A 2
B. MULTIPLY BY 2
C. FOIL
D. NOTHING, IT'S FINE
3/4
Got it!
You have jumped to the correct answer
Next
3/4
What are the factors of the following?
A. 2(a+7i)2
B. (a+7i)(a-7i)
C. 2(a+7)(a-7)
D. 2(a+7i)(a-7i)
4/4
WELL DONE!
You have earned one more pixel coin. You have two left to pay the King of the castle.
Continúa
4/4
Error
Wow! It seems like the answer is incorrect.
Return
ERROR
Wow! It looks like the answer is incorrect.
Return
ERROR
Wow! It seems like the answer is incorrect.
Return
ERROR
Wow! It looks like the answer is incorrect.
Go back
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
COINS
Dancing stones
PIXELrolls
You must maintain balance and jump from one roller to another by answering the questions correctly in order to progress.
Start
In the following example, the "50" is not a perfect square. Can we still use the Sum of Squares technique?
YES
NO
1/5
We must take the square root of 50 to find the "b" part in our pattern. What does it reduce to?
does not reduce
2√5
5√2
2/5
What are the factors of the following?
(x+5i)(x-5i)
(x+5i√2)(x-5i√2)
(x+5√2)(x-5√2)
3/5
When trying to find the factors of this quadratic, we must take the square root of 18 to find the "b" part. What does √18 reduce to?
3√6
2√3
3√2
4/5
Using the Sum of Squares technique, what are the factors of the following?
(x+3i√2)(x-3i√2)
(x+2i√3)(x-2i√3)
(x-3i√2)2
5/5
WELL DONE!
You have earned one more pixel coin. You need one more to pay the King of the castle.
Continue
5/5
ERROR
Oh! It seems you got soaked
Return
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Dancing stones
Choose the right stones and stand on them while answering the questions correctly to move forward without falling into the water.
Start
Let's go!
Choose a rock to jump on
1/5
In the following example, we must use the Difference of Squares. Which of the following is the pattern for this?
(a+b)(a-b)
(a+bi)(a-bi)
a2 + 2ab + b2
1/5
Let's go!
Choose a rock to jump on
2/5
Using the Difference of Squares, we must take the square root to find "a" and "b". Fill in the pattern.
(x + 9)(x - 9)
(x2 + 9)(x2 - 9)
(x + 9i)(x - 9i)
2/5
Let's go!
Choose a rock to jump on
3/5
SO, we have seen that our x4 factors into smaller quadratics. If we tried to factor the (x2 + 9), we will get an answer of....
(x2 + 9)(x2 - 9)
(x-3i)2
(x+3)(x-3)
(x+3i)(x-3i)
3/5
Let's go!
Choose a rock to jump on
4/5
Now that we've found the complex number part, let's find the real number part. Factor (x2 - 9)
(x+3i)(x-3i)(x2 - 9)
(x+3)(x-3)
(x+3i)(x-3i)
(x+3)(x-6)
4/5
Let's go!
Choose a rock to jump on
5/5
Putting it all together, what are the factors of:
(x+3)2(x-3)2
(x+3i)(x-3i)(x+3)(x-3))
(x+3i)2(x-3i)2
5/5
WELL DONE!
It seems you have obtained the 4 pixel coins, talk to the Castle King to be released
Continue
5/5
Error
Oh! It looks like you got soaked
Return
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
use coins
Good!
King Pixel has finally set you free! You can now see the sunset at the lake.
Let's go!
YOU HAVE ESCAPED AND YOU ARE FREE!
Now you can enjoy the pleasant view of the lake at sunset
Start over
YOU ARE NOT READY YET You must complete the previous missions to continue
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
NOT YET READY You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue
Factoring over the Complex Numbers Escape!
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Created on October 29, 2025
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Transcript
Escape from Pixel Castle
Start
Introduction
While you are traveling through unexplored areas of China, you have been captured by the soldiers of the Pixel King's Castle. You will need to gather courage and overcome the trials that the King will put you through in order to try to obtain the pixel coins, pay for your release with them, and continue your journey.
Let's go!
select mission
PIXEl rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Fake doors
You must correctly answer the various questions to find the only true door and advance in your mission.
Start
WHAT TYPE OF SOLUTION WOULD THE FOLLOWING HAVE:
INFINITE SOLUTION
REAL NUMBERS
COMPLEX NUMBERS
1/3
Great!
You chose the correct door
Next
1/3
What is the general form when factoring over the complex numbers?
(a+b)(a-b)
(a+bi)(a-bi)
(a+b)2
2/3
Take it!
You chose the correct door
Next
2/3
When using the Sum of Squares Pattern, how do we find "a" and "b"?
Take the Square Root of a2 and b2
Divide by "a" and "b"
Complete the Square
3/3
Well done!
You have a pixel coin! Three more will be enough to buy your freedom
Continues
3/3
ERROR!
Ouch! What a headache.Try again.
Return
ERROR!
Ouch! What a headache.Try again.
Return
Error!
Ouch! What a headache.Try again.
Return
MISSION MAPS
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Maths jump
Solve math calculation problems to advance in this mission. Jump on the correct answer and demonstrate your skills.
Start
Easy one first!What are the factors of:
A. (x+6)2
B. (x+6)(x-6)
C. (x+6i)(x-6i)
D. (x-6i)2
1/4
Well done!
You have jumped to the correct answer
Next
1/4
What are the factors of?
A. (3x+5)(3x-5)
B. (3x+5i)(3x-5i)
C. (3x+5i)2
D. (5x+3i)(5x-3i)
2/4
Yeah!
You have jumped on the correct answer
Next
2/4
In the following example, what must you do first in order to factor over the complex numbers?
A. FACTOR OUT A 2
B. MULTIPLY BY 2
C. FOIL
D. NOTHING, IT'S FINE
3/4
Got it!
You have jumped to the correct answer
Next
3/4
What are the factors of the following?
A. 2(a+7i)2
B. (a+7i)(a-7i)
C. 2(a+7)(a-7)
D. 2(a+7i)(a-7i)
4/4
WELL DONE!
You have earned one more pixel coin. You have two left to pay the King of the castle.
Continúa
4/4
Error
Wow! It seems like the answer is incorrect.
Return
ERROR
Wow! It looks like the answer is incorrect.
Return
ERROR
Wow! It seems like the answer is incorrect.
Return
ERROR
Wow! It looks like the answer is incorrect.
Go back
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
COINS
Dancing stones
PIXELrolls
You must maintain balance and jump from one roller to another by answering the questions correctly in order to progress.
Start
In the following example, the "50" is not a perfect square. Can we still use the Sum of Squares technique?
YES
NO
1/5
We must take the square root of 50 to find the "b" part in our pattern. What does it reduce to?
does not reduce
2√5
5√2
2/5
What are the factors of the following?
(x+5i)(x-5i)
(x+5i√2)(x-5i√2)
(x+5√2)(x-5√2)
3/5
When trying to find the factors of this quadratic, we must take the square root of 18 to find the "b" part. What does √18 reduce to?
3√6
2√3
3√2
4/5
Using the Sum of Squares technique, what are the factors of the following?
(x+3i√2)(x-3i√2)
(x+2i√3)(x-2i√3)
(x-3i√2)2
5/5
WELL DONE!
You have earned one more pixel coin. You need one more to pay the King of the castle.
Continue
5/5
ERROR
Oh! It seems you got soaked
Return
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
Dancing stones
Choose the right stones and stand on them while answering the questions correctly to move forward without falling into the water.
Start
Let's go!
Choose a rock to jump on
1/5
In the following example, we must use the Difference of Squares. Which of the following is the pattern for this?
(a+b)(a-b)
(a+bi)(a-bi)
a2 + 2ab + b2
1/5
Let's go!
Choose a rock to jump on
2/5
Using the Difference of Squares, we must take the square root to find "a" and "b". Fill in the pattern.
(x + 9)(x - 9)
(x2 + 9)(x2 - 9)
(x + 9i)(x - 9i)
2/5
Let's go!
Choose a rock to jump on
3/5
SO, we have seen that our x4 factors into smaller quadratics. If we tried to factor the (x2 + 9), we will get an answer of....
(x2 + 9)(x2 - 9)
(x-3i)2
(x+3)(x-3)
(x+3i)(x-3i)
3/5
Let's go!
Choose a rock to jump on
4/5
Now that we've found the complex number part, let's find the real number part. Factor (x2 - 9)
(x+3i)(x-3i)(x2 - 9)
(x+3)(x-3)
(x+3i)(x-3i)
(x+3)(x-6)
4/5
Let's go!
Choose a rock to jump on
5/5
Putting it all together, what are the factors of:
(x+3)2(x-3)2
(x+3i)(x-3i)(x+3)(x-3))
(x+3i)2(x-3i)2
5/5
WELL DONE!
It seems you have obtained the 4 pixel coins, talk to the Castle King to be released
Continue
5/5
Error
Oh! It looks like you got soaked
Return
MISSION MAP
PIXEL rolls
Fake doors
MATHS JUMP
coins
Dancing stones
use coins
Good!
King Pixel has finally set you free! You can now see the sunset at the lake.
Let's go!
YOU HAVE ESCAPED AND YOU ARE FREE!
Now you can enjoy the pleasant view of the lake at sunset
Start over
YOU ARE NOT READY YET You must complete the previous missions to continue
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
NOT YET READY You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue
Be careful!
If you go back to the beginning, you will lose all progress and have to start over.
Continue
Exit
YOU ARE NOT READY YET You must complete the previous missions to continue