1. Warm-Up DEGREE is Even/Odd, LEADING COEFFICIENT is Positive/Negative,
END BEHAVIOR
EXTREMA (Max or Min, Relative or Absolute)
(-2, 15)
EVEN
(2) POS
(3) END BEHAVIOR x  ±∞; f(x)  ∞
(4) A. Min: (7, -21)
R. Min: (-9, -8) R. Max: (-2, 15)
[1]
ODD
(2) NEG
(3) END BEHAVIOR x  - ∞; f(x)  ∞
x  ∞; f(x) - ∞
(4) R. Min: (-3, 4) R. Max: (8, 9)
[2]
(8, 9)
(-3, 4)
(-9, -8)
(7, -21)
[3]
[4]
EVEN
NEGATIVE
END BEHAVIOR
Absolute Max: Relative Max: Relative Min:
ODD
POSITIVE
END BEHAVIOR
Relative Max: Relative Min:

2. Factoring Polynomials Review:
[1] Difference of SQUARES
Example
[2] Difference of CUBES
Example
[3] Sum of CUBES
Example

3. [4] Factoring Trinomials:
ax2 + bx + c
Example
Step #1: Find the factor pair (n1 and n2) that MULTIPLY = ac (outsides) and ADD = b (middle).
Step #2: Split the middle term bx = n1x + n2x
Step #3: Perform factor by grouping on
ax2 + n1x + n2x + c
GCF of ax2 + n1x and GCF n2x + c
= (?x + ?) (?x + ?)
Multiply = -12| Add = -4
-6 * 2 = 12; = -4

4. Factoring Polynomials: PRACTICEb) c) d) e) f)

5. U – SUBSTITUTION: u = xn ax2n + bxn + c = 0 au2 + bu + c = 0
Step #1: Must have a trinomial in which one power of x is DOUBLE the other.
ax2n + bxn + c = 0
Step #2: Let u equal smaller exponent of x
u = xn
Step #3: SUBSTITUTE u into the trinomial to create a quadratic equation.
au2 + bu + c = 0
Step #4: Use FACTORING or QUADRATIC FORMULA to find roots for u and solve for xn.
u = Root #1 and u = Root #2  xn = Root #1 and Root #2

6. x4 – 16x2 + 60 = 0 EXAMPLE of U – SUBSTITUTION:
Step #1: x4 is double the x2 exponent
Step #2: u = x2
Step #3: u2 – 16u +60 = 0
Step #4: Solve u2 – 16u +60 = 0
Factoring: (u – 10)(u – 6)=0
Roots: u = 10 and u = 6  x2=10 and x2=6
Solve for x:

7. x7 is more than double x2 power
Example 1: Quadratic Form Only
If possible, identify the variable term for u and write each equation in quadratic form using U-SUBSTITUTION.
a) 2x6 + x3 + 9 = 0
b) x4 + 2x = 0
Let u = x3,
2u2 + u + 9 = 0
Let u = x2,
u2 + 2u + 10 = 0
c) 7x10 – 6 = 0
d) x7 + 2x = 0
Not Possible:
No second x term to use
Not Possible:
x7 is more than double x2 power f) e)
Let ,
u2 - 2u + 8 = 0
Let ,
u2 - 5u + 10 = 0

8. Example 2: Solve using U-SUBSTITUTION
Check to factor substituted quadratic form. b) a)

9. Example 2: U-Substitution Part 2
Check to factor substituted quadratic form. c) d)

10. Example 2: U-Substitution Part 3
Check to factor substituted quadratic form. f) e)
Cannot square -4 …because there is no number that multiples by itself to equal -4

11. Example 2: U-Substitution Part 4
Check to factor substituted quadratic form. g) h) i) j)

12. Example 3: Solving Equations of Perfect Cubes
Factor and Apply Quadratic Formula b) a) c) d)