Transcript 6 -6 Factoring by Grouping - Fayette County Public Schools

5 minutes
Warm-Up
Collect like terms and arrange in descending
order.
1) 4x3 + 6x4 – 2x4 + 8x
2) 3x – 5x + 5 + 2x0
3) Evaluate 4x3 + x2 – 2 for x = 0 and x = 1
Addition / Subtraction of
Polynomials
Objectives:
•To add polynomials
•To subtract polynomials
Example 1
Add
(5x2 + 3x + 4) + (3x2 + 5)
= 8x2 + 3x + 9
Example 2
Add
(7x2y3 + xy) + (1 – 2x2y3)
= 5x2y3 + xy + 1
Practice
Add.
1) (3x2 + 2x – 2) + (-2x2 + 5x + 5)
2) (31x4 + x2 + 2x – 1) + (-7x4 + 5x3 – 2x + 2)
3) (4a2b – 5a + 3) + (-2a2b – 2a – 4)
Example 3
Add.
(2x4 – 5x2 + 4x + 5) + (5x4 + 7x3 – 2x2 – 2x)
2x4 + 0x3 – 5x2 + 4x + 5
5x4 + 7x3 – 2x2 – 2x + 0
7x4 + 7x3 – 7x2 + 2x + 5
Example 4
Add.
(-3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1) + (5x5 – 3x3y3 – 5xy5)
-3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1
5x5
- 3x3y3
- 5xy5
5x5 – 3x4y3 + 3x3y3 – 6x2
+1
Practice
Add.
1) (-2m3 – 5m2 – 2m – 4) + (m4 – 6m2 + 7m – 10)
2) (-3x4y3 – 5xy + 2) + (x4y3 + x2 + 2xy + 5)
Subtraction of
Polynomials
Objectives:
•To subtract polynomials
Example 1
Subtract.
(5x2 + 3x - 2) - (2x2 + 1)
= 5x2 + 3x - 2 - 2x2 - 1
= 3x2 + 3x - 3
Example 2
Subtract.
(2x2y2 + 3xy3 – 4y4) - (x2y2 – 5xy3 + 3y – 2y4)
= 2x2y2 + 3xy3 – 4y4 - x2y2 + 5xy3 – 3y + 2y4
= x2y2 + 8xy3 – 2y4 – 3y
Practice
Subtract.
1) (5x4 + 4) – (2x2 – 1)
2) (-7m3 + 2m + 4) – (-2m3 – 4)
3) (-3a2b4 + 5ab - 4) - (-4a3 + 11a2b4 – 2a - 6)
Example 3
Subtract.
(8x3 + 6x2 – 3x + 5) – (5x3 – 3x2 + 2x – 4)
8x3 + 6x2 – 3x + 5
-5x3 + 3x2 - 2x + 4
3x3 – 9x2 - 5x + 9
Example 4
Subtract.
(2a4b + 5a3b2 – 4a2b3) – (4a4b + 2a3b2 – 4ab)
2a4b + 5a3b2 – 4a2b3
-4a4b - 2a3b2
+ 4ab
-2a4b + 3a3b2 – 4a2b3 + 4ab
Practice
Subtract.
1) (-2m3 – 5m2 – 2m – 4) - (m4 – 6m2 + 7m – 10)
2) (-3x4y3 – 5xy + 2) - (x4y3 + x2 + 2xy + 5)
RULE!
• In order to add or subtract, you must
have ….
• The same BASE and the same
EXPOENNT!
Example
• You can add 3x2 + 2x2 together
• You CAN NOT add 3x3 + 2x2
together!