Exponential Rules
Simplify: (x3)5
x15
Factor the expression x2 - 49.
(x + 7)(x - 7)
What is the value of i?
i = √-1
State the quadratic formula for solving 0 = ax2 + bc + c.
x = [-b ± √(b2 - 4ac)] / (2a)
What is the formula for the discriminant?
b2 - 4ac
Simplify: y2y7
y9
Factor the expression 4y2 + 12y + 9.
(2y + 3)2
Simplify √-81
9i, -9i
Identify the values of a, b and c for the equation:
x2 - 5x + 6 = 0
a = 1, b = -5, c = 6
If the discriminant is 25, what is the nature of the solutions?
2 real solutions
Simplify: (2a2b−3)3
8a6/b9
Factor 4x3 - x completely.
x(2x + 1)(2x - 1)
Simplify (3 + 5i) + (7 - 2i).
10 - 3i
Use the formula to find the real solutions to the equation 0 = x2 + 5x + 4.
x = -1, x = -4
Calculate the discriminant for the equation 3x2 - 2x + 1 = 0
-8
Simplify 40 + 4-1
1 1/4 or 5/4
Factor x4 - 1
(x2 + 1)(x + 1)(x - 1)
or
(x + i)(x - i)(x + 1)(x - 1)
Simplify (2 + i)(3 - 4i)
10 - 5i
If a quadratic equation has a negative discriminant, what are the nature of the solutions?
2 complex solutions
Determine the nature of the solutions for 9x2 - 12x + 4 = 0.
One real solution
Simplify the expression:
18m5n-2 / 6m2n4
3m3 / n6
Factor 18x2 + 98.
2(3x + 7i)(3x - 7i)
What is the complex conjugate of a + bi?
a - bi
Use the quadratic formula to find the real solutions to the equation 0 = x2 - 4x + 8.
x = 2 + 2i, x = 2 - 2i
If a discriminant is 0, which is true?
a. The polynomial is a difference of squares.
b. The polynomial is a sum of squares.
c. The polynomial is a perfect square trinomial.
d. The polynomial cannot be factored.
c. The polynomial is a perfect square trinomial.