Period 2 Chapter 6 Retake Review

degree 2: quadratic, degree 3: cubic
degree 4: quartic, degree 5: quintic

1 term: linear, 2 terms: binomial, 3 terms: trinomial

1A. x^5 - x^3 + x, quintic, trinomial

1B. 4x^3 + 2x^2 + 2x, cubic, trinomial

2A. y = (2.04x10^-4)x^3 + .26 x^2 - 3.62 x + 29.3

2B. $414.93

Imaginary zeros/roots come in pairs called CONJUGATES.

3A. x^3 - 4 x^2 - 11 x + 30

3B. x^3 + 6 x^2 + 9 x + 54

To find the zeros of a function, FIRST MAKE IT EUQAL TO ZERO, then SOLVE FOR x.

Multiplicity: THE NUMBER OF TIMES A FACTOR OR ZERO APPEARS

4A. x = -1 (mult. of 2), x = 3/5 (mult. of 1)

4B. x = 0 (mult. of 1), x = 2 (mult. of 3), x = -1/2 (mult. of 1)

FACTORING CHECK LIST:
1. Check for a GREATEST COMMON FACTOR. Continue factoring.

2. Check for a DIFFERENCE OF TWO SQUARES. Continue factoring.
Pattern: a^2 - b^2 = (a + b)(a - b)

3. Check for a SUM OR DIFFERENCE OF TWO CUBES.
Pattern: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Pattern: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

4. Check for a SUBSTITUTION TO MAKE A NICE QUADRATIC.

5A. 3x^2 (x - 2)(x + 1) =0
x = 0, x = 2, x = -1

5B. 4x (x + 5)(x - 2) = 0
x = 0, x = -5, x = 2

6A. 2 (x + 3)(x^2 - 3x + 9) = 0
x = -3, x = (-3 +/- 3i sqrt3) / 2

6B. (2x - 5)(4x^2 + 10x + 25) = 0
x = 5/2, x = (-5 +/-5i sqrt5) / 4

7A. (x + 10)(x - 10) = 0
x = -10, x = 10

7B. 3 (x + 4)(x - 4) = 0
x = -4, x = 4

8A. 2(x^2 - 14)(x^2 + 1) = 0
x = +/- sqrt14, x = +/- i

8B. (x^2 + 3)(x^2 + 5) = 0
x = +/- i sqrt 3, x = +/- i sqrt5

9A. (x + 1)(x - 3)(x - 4)

9B. (x - 3)(x - 3)(x + 2)

10A. complex roots: 3, possible real roots: 1, 3

10B. complex roots: 4, possible real roots: 0, 2, 4

11A. This is really tough! Don't even try p/q--it won't work because the last term is 36x. Instead, look for a GCF, then go through the rest of the factoring check list.
x = 0, x = +/- 3, x = +/- 2i

11B. This is also tough! Look for a GCF, then go through the rest of the factoring check list.
x = +/- sqrt14, x = +/- i

12A. x = -4, x = +/-i sqrt7

12B. x = -2, x = 1 +/- sqrt7