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Solving by Backtracking
Solving using the Zero Product Property
Inverses
Ciphers
100
2x + 7 = -23
-15
100
x(x+1) = 0
0 or -1
100
What is another word for "additive inverse"?
opposite
100
Encipher "hi" using the Caesar cipher C = P + 2 (mod26).
JK
200
x^2 + 5 = 30
5 or -5
200
(2x + 1)(x - 3) = 0
-1/2 or 3
200
What is another word for "multiplicative inverse?"
reciprocal
200
Encipher "hi" using the affine cipher C = 5P + 1 (mod26).
KP
300
(x+3)^2 + 2 = 38
3 or -9
300
x^2 + 7x + 12 = 0
-3 or -4
300
Find the inverse function for: y = (2x - 3)/5
y = (5x + 3)/2
300
Is the affine cipher C = 14P + 1 (mod26) invertible? How can you tell?
It is not invertible, because the multiplier (14) shares a factor with the mod (2) and has no reciprocal.
400
2(x - 2)^2 + 2 = 2
2
400
x^2 - x = 6
-2 or 3
400
What is the reciprocal of 17 in mod26?
23
400
Solve for P in the affine cipher C = 17P +1 (mod26).
P = 23(C - 1)
500
(sqrt(x + 5) - 2)/3 = 1
20
500
x^3 + 2x^2 = 15x
0, 3, or -5
500
Find the reciprocal of 7 in mod8.
7
500
Decipher the message "VHF NJQ," which was enciphered using the affine rule C = 17P + 3.
YOU WIN