Factoring Polynomials & Rational Expressions
Factor the expression completely:
6x2 - 15x
3x(2x - 5)
When do we need to use a "plus or minus" symbol?
When we take the square root of our variable squared
What is the imaginary number, i, equal to?
i = sqrt(-1)
What is the discriminant?
The part under the square root: b2 - 4ac
What kind of transformation is indicated by a negative sign?
Reflection or "flip"
How can we determine which numbers to exclude from the domain of a rational function?
Set the denominator equal to 0 and solve for x
When your exponent is a fraction, what do the numerator and denominator each represent?
Power over Root
Simplify the radical expression:
sqrt(45)
3 sqrt(5)
How many x-intercepts does your parabola have if the discriminant is positive?
2
What kind of transformation is indicated by addition and subtraction?
Shift
Solve the equation:
x2 - 4x = 5
x = -1, 5
Find all solutions:
2x2 = 50
x = 5, -5
Subtract the complex numbers:
(-3 + 2i) - (3 - 5i)
-6 + 7i
How many x-intercepts does your parabola have if the discriminant is negative?
0
Use the words ' horizontal' and 'vertical' to make the following statement true:
Function transformations that appear inside the function are in the direction (and reversed!); transformations that appear outside the function are in the direction.
horizontal; vertical
What numbers must be excluded from the domain of this rational function?
f(x) = (x + 3)/(x2 - 5x + 6)
2, 3
Evaluate without a calculator:
642/3
16
Simplify the radical expression:
sqrt(-28) + sqrt(-63)
5i sqrt(7)
Solve using the Quadratic Formula:
x2 + 8x = -16
x = -4
Give the parent function and describe the transformations on the following function:
g(x) = (x + 3)3 - 8
Parent: f(x) = x3
Shifted Left 3 and Down 8
Simplify the rational expression:
(15x2 + 58x - 8)/(2x2 - 32)
(15x - 2)/2(x - 4)
Find all solutions:
(x + 2)4/3 = 81
x = -29, 25
Divide the complex numbers. Be sure to rationalize your result!
(5 - i)/(2 + i)
9/5 - 7i/5
Solve using the Quadratic Formula:
x2 = 2x - 17
x = 1 + 4i, 1 - 4i
If the parent function, f(x), passes through the point (1, 1), find its corresponding point on the transformed function:
g(x) = -f(x - 2) - 3
(3, -4)