The document provides reminders about Khan Academy assignments due, notes that a new study guide is available on factoring, and informs students that there will be a test this Friday covering factoring techniques like grouping and solving trinomials of the form (x^2 + bx + c) and (ax^2 + bx + c).
2. Reminders:
1. Khan Academy due Yesterday. You did not have to
do the Factoring by Grouping Topic (Due this Week).
You can complete the topics by this Wednesday for
80% max.
2. New Study Guide Available on Factoring in both PDF
and PPT formats.
3. Test this Friday on Grouping, (x2 + bx + c) trinomials
and (ax2 + bx + c) trinomials.
3. Warm Up
1. What structure has the record for most years as the
world's tallest, and how tall is it (in feet) ?
The great pyramid of Giza, Egypt, at 455 feet
2. For how many years did it hold the record?
4,109 years. From 2560 B.C., to 1549 A.D
(St. Olaf's Cathederal in Europe).
4.
5. Warm Up
3. How tall (in ft.) is the Burj Khalifa,
now the world's tallest building? 2,722 feet.
4. How tall (in ft.) is Mt. Tapochau? 1,555 feet.
5. What percent of Mt. Tapochau's height is the Burj
Khalifa? (round each height to the nearest 10 feet)
174%, or Mt. Tapochau plus another 3/4ths of a
Mt. Tapochau stacked on top of it.
9. The Building is so tall,
you can see the sun set
twice in the same day.
10. How are 2 sunsets possible in the same day?
Because of the curvature of the
Earth, you can only see to the horizon.
The higher you are, the farther you can
see.
Is there a formula for that?
(In miles)
6. How far can you see if you are 10 ft. above sea level?
Round to nearest mile
7. How many miles can you see if you're at the top of
the Burj? Round to nearest mile
11.
12. Test Prep
1. What is the highest degree in the
prime factorization of 72?
2. What is the GCF of 12x4y2 and 28x2y5?
13. Factoring: ax2 + bx + c
These trinomials are different because they have a
coefficient in the squared term. You will use a form of
grouping to solve. The more factors there are for a given
number, the more possibiities there are for a
solution, and thus the more time it can take to solve.
Example 1: 3x2 +14x + 8 Step 1: Look for GCF to Factor out.
We are going to replace the middle term 14x, with
two terms. The polynomial will have 4 terms
and we can then solve by grouping.
But what 2 terms do we replace the 14x with?
First, the terms must equal 14x, or we would be
solving a problem different from the one given.
14. Factoring: ax2 + bx + c
3x2 +14x + 8
Step 2: We multiply ac together and get 24.
Step 3: Look for factors whose product is 24 and
whose sum is 14
Step 4: Replace the one middle term with the two new
terms, being careful to use the correct signs.
Step 5: Solve using the factoring by grouping method.
3x2 + 12x + 2x + 8 (3x2 + 12x) + (2x + 8)
Final Answer: (x + 4)(3x + 2)
15. Factoring: ax2 + bx + c
Example 2: ( 25x2 + 20x + 4) Step 1: Look for GCF
Step 2: We multiply ac together.
Step 3: Look for factors whose product is 100 and
whose sum is 20
Step 4: Replace the one middle term with the two new
terms, being careful to use the correct signs.
Step 5: Solve using the factoring by grouping method.
Final Answer: (5x + 2)(5x + 2) or (5x + 2)2