# Warm-Up DEGREE is Even/Odd, LEADING COEFFICIENT is Positive/Negative,

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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:

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

[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

Factoring Polynomials: PRACTICE
b) c) d) e) f)

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

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:

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

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

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

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

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

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