1. What is the ﬁrst step in any factoring problem?
2. What is the ﬁrst step to factor -x2 + 8x - 15?
3. On a test, Luis Gonzalez wrote the following, but the teacher
considered it to be incomplete. Explain why.
15x2 - 21x - 18 = (5x + 3)(3x - 6).
Step 1. Always check for the _________________ ﬁrst.
Step 2. Is the expression a -termed expression?
If yes, then try one of these three forms:
Step 3. If it is a -termed expression (or trinomial), it may fall into one
of these groups:
1. The coefﬁcient of is 1. Example: ________________. Find two
numbers whose sum is ______ and whose product is ______. They are
______ and ______:
2. The coefﬁcient of is not 1. Example: ________________.
a. Find the product of ﬁrst and last coefﬁcients: ___________ =
b. Look for two numbers whose product is ______ and whose sum is
_____: _____ and ______.
c. Write the expression as four terms:
d. Proceed to use Step 4 as follows:
Step 4. If it is a -termed expression, try factoring by grouping.
A person is standing at the top of a building, and throws a ball upwards
from a height of 60 ft, with an initial velocity of 30 ft per second. How
long will it take for the ball to reach a height of 25 ft from the ﬂoor?
Use the formula
If ax2 + bx + c = 0 and a ≠ 1, then
Solve the equations. Use the quadratic formula.
1. Consider equations and
Do their solutions have to be the same? Explain your answer.
2. Consider and
Are the solutions the same for both equations? Explain.
3. What is a Reference Angle?
The Reference angle for θ is the acute angle θR that the terminal side of
θ makes with the x-axis.
Find the reference angle θR for θ, and sketch θ and θR in standard position.
a) θ = 315o b) θ = -240o
c) θ = 5π/6 y
Multiply degrees by to get radians.
Multiply radians by to get degrees.
Find the exact values of sin θ, cos θ and tan θ if
(a) θ = 5π/6 (b) θ = 315o
Verifying Trigonometric Identities.
The fundamental identities.
1. The Reciprocal Identities.
2. The Tangent and Cotangent Identities.
3. The Pythagorean Identities.
Show that the following equation is an identity by transforming the left-hand side
into the right-hand side: