Daily Warm-UP Quiz

Factor completely:

1. x4 – 17x2 +722. x4 + 12x2 +363. x4 – 7x2 +124. x8 – 815. x6 – 256. x6 – 36

Quiz (NO notes!)

1. Write your first ten perfect cubes. EX. 13 = __ 23= __ 33= __ etc.2. Given the function f(x) = (x+3)3, describe the appearance of the graph w/o actually graphing.3. Factor completely: x3 + 27

1. Write your first ten perfect cubes.

EX. 13 = __ 23= __ 33= __ etc.

2. (x-5)3 = _______________

3. Factor completely:

x3 -125 -15x2 +75x

4. Divide using long division:

÷ x -5

5. x3 – 53 = ________________________

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:

Check Your Answer Using Multiplication:

(x-3) (x3 + 3x2 + 9x + 27) =

Check your answer here!

Checking for Understanding

Divide  2x4 + 4x3 - 5x2 + 2x – 3 by x2 + 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.

(5x4 + 18x3 + 10x2 + 3x) x2 + 3x

(x3 + 6x2 - 5x + 20)x2 + 5

Daily Warm-UP QuizHonors

Algebra 2 is child’s

play compared

to this workout!

1. Factor completely:a. x3 – 27 b. x3 + 64

2. Multiply: a. (x + 3)3 b. (x -2) 3

3. Simplify: b. √-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 + 2x2 - 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)

FACTORTHEOREM

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) = 2x3 + 11x2 + 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) = 2x3 + 6x2 – 8 at x = 1. 4. Factor 2x3 + 6x2 – 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-3 x4 -0x3 + 0x2 + 0x1 -81

x3

x4 - 3x3(-)

+ 3x2

3x3 + 0x2

3x3 - 9x2(-)

9x2 + 0x1

+ 9x

9x2 – 27x1(-)

27x1 -81

+ 27x

27x1 -81(-) Return to

lesson!