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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) [1] [2] (8, 9) (-3, 4) (-9, -8) (7, -21) [3] [4]

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**Factoring Polynomials Review:**

[1] Difference of SQUARES Example [2] Difference of CUBES Example [3] Sum of CUBES Example

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**[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

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**Factoring Polynomials: PRACTICE**

b) c) d) e) f)

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**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

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**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:

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**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 c) 7x10 – 6 = 0 d) x7 + 2x = 0 f) e)

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**Example 2: Solve using U-SUBSTITUTION**

Check to factor substituted quadratic form. b) a)

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**Example 2: U-Substitution Part 2**

Check to factor substituted quadratic form. c) d)

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**Example 2: U-Substitution Part 3**

Check to factor substituted quadratic form. f) e)

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**Example 2: U-Substitution Part 4**

Check to factor substituted quadratic form. g) h) i) j)

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**Example 3: Solving Equations of Perfect Cubes**

Factor and Apply Quadratic Formula b) a) c) d)

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Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.

Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.

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