Daily Warm-UP Quiz Factor completely: 1. x 4 – 17x 2 +72 2. x 4 + 12x 2 +36 3. x 4 – 7x 2 +12 4. x 8 – 81 5. x 6 – 25 6. x 6 – 36.

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Daily Warm-UP Quiz Factor completely: 1. x 4 – 17x 2 +72 2. x 4 + 12x 2 +36 3. x 4 – 7x 2 +12 4. x 8 – 81 5. x 6 – 25 6. x 6 – 36

Quiz (NO notes!) 1.Write your first ten perfect cubes. EX. 1 3 = __ 2 3 = __ 3 3 = __ etc. 2. Given the function f(x) = (x+3) 3, describe the appearance of the graph w/o actually graphing. 3. Factor completely: x 3 + 27

1.Write your first ten perfect cubes. EX. 1 3 = __ 2 3 = __ 3 3 = __ etc. 2. (x-5) 3 = _______________ 3. Factor completely: x 3 -125 -15x 2 +75x 4. Divide using long division: ÷ x -5 5. x 3 – 5 3 = ________________________

Dividing Polynomials At the end of this two-part lesson, you should be able to:  Divide polynomials using long division  Divide polynomials using synthetic division

PART I: DIVIDING POLYNOMIALS USING LONG DIVISION Divide:

Checking for Understanding Divide 2x 4 + 4x 3 - 5x 2 + 2x – 3 by x 2 + 2x + 3 Check:

Determining Polynomial Factors You can use long division to determine the factors of a polynomial! ALERT!

Determine whether each divisor is a factor of each dividend. Explain. (5x 4 + 18x 3 + 10x 2 + 3x) x 2 + 3x (x 3 + 6x 2 - 5x + 20) x 2 + 5

Daily Warm-UP Quiz Honors Algebra 2 is child’s play compared to this workout! 1. Factor completely: a.x 3 – 27 b. x 3 + 64 2. Multiply: a. (x + 3) 3 b. (x -2) 3 3. Simplify: a.√-25 b. √-50 c. √-16 d. √-48 e. -8 +/- √-48 f. -15 +/- √-50 16 30

PART II: DIVIDING POLYNOMIALS USING SYNTHETIC DIVISION When a divisor is of the form _______, where c is a constant, _____________ can be used. ALERT! x c synthetic division

Synthetic Division Divide using synthetic division: (x 3 + 2x 2 - 4x + 8) ÷ (x + 2) Step 1: Check to determine that the divisor is of the form x + c or x – c. Step 2: Determine the zero, based upon the divisor, to set up the problem using synthetic division.

Synthetic Division 1 2 - 4 8 Zero -2 Remainder To check your answer, multiply the quotient by the divisor and add the remainder. It should be the same as the original polynomial.

Divide using synthetic division:

REMAINDER THEOREM If a polynomial f(x) is divided by (x - k), the remainder is r = f(k). Without dividing, determine the remainder of (x 3 + 2x 2 - 4x + 8) ÷ (x + 2)

FACTOR THEOREM A polynomial, f(x) has a factor (x- k) if and only if f(k) = 0. Determine if x + 2 is a factor of (x 3 + 2x 2 - 4x + 8)

Final Checks for Understanding 1.Given that f(x) = 2x 3 + 11x 2 + 18x + 9 has x = -3 as a zero, factor f(x). 2.What kind of divisor is required for synthetic division? 3.Evaluate f(x) = 2x 3 + 6x 2 – 8 at x = 1. 4.Factor 2x 3 + 6x 2 – 8 completely. 5.Write the polynomial divisor, dividend, and quotient that the synthetic division below represents: 2 6 0 -8 2 8 8 2 8 8 0 1

Homework

PART I: DIVIDING POLYNOMIALS USING LONG DIVISION Divide X-3x 4 -0x 3 + 0x 2 + 0x 1 -81 x3x3 x 4 - 3x 3 (-) + 3x 2 3x 3 + 0x 2 3x 3 - 9x 2 (-) 9x 2 + 0x 1 + 9x 9x 2 – 27x 1 (-) 27x 1 -81 + 27x 27x 1 -81 (-) Return to lesson!lesson

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