CPPC Chapter 2A Test Review

Solving Equations

100

#2 Solve:

x² + 8x + 25 = 0

-4 +/- 3i

200

#7 What is the vertex of the following quadratic function?

f(x) = x² - 2x - 3

(1, -4)

300

#23 Find the value for k given g(x) = x³ + 4x² - kx + 8

k=-4

400

Write the quartic function f(x) in completely factored form that has zeros -2, -4, 3, and 0 and f(-1) = 4

1/3x(x+2)(x+4)(x-3)

500

#18 Given the following x and y values, find the linear model AND the quadratic model

x: 0, 1, 2, 3, 4, 5, 6

y: 7.62, 7.51, 7.56, 7.78, 8.16, 8.71, 9.43

linear: 0.30x + 7.21

quadratic: 0.083x² - 0.197x + 7.62

Zeros and Multiplicity

100

#1 What is the multiplicity of the zero (-3,0)?

f(x) = 3x⁴(x-1)²(x+3)⁵(x-3)³

5

200

#9 If you know that a quartic function has zeros 2+i and i, determine the other zeros

2-i and -i

300

#22 Find the number of complex zeros for the follow equation:

f(x) = 2x⁵ - 7x⁴ + 10x³ - 5x² - 2x + 2

5 (biggest exponent)

400

#3 What is the maximum number of real zeros possible for the following function:

f(x) = 3x⁴ + ax³ - bx² + 12x - 2

4 (number of sign changes in f(x) and f(-x))

500

#11 Find all the zeros of the function by factoring:

f(x) = x⁴ - 3x² - 4

+/- 2, +/- i

Imaginary and Complex Numbers

100

#17: Find all real solutions of x⁴ - 4x³ + 12x - 9 = 0

x = 1, 3 +/- root3

200

#4 Write the expression in standard form:

(-4 - 3i) - (-8 + 2i)

4 - 5i

300

#5 Divide and write in standard form:

2/(1 + i)

1 - i

400

#6 Simplify and write in standard form:

(1/i⁶) + i¹⁹

-1 - i

500

#14 Find the cubic polynomial in factored form, irreducible over the reals, with the following zeros: -1, 1-i

f(x) = (x+1)(x²-2x+2)

Other

100

#16 If one of the zeros of a quadratic function is 3+i, find the quadratic function

x² - 6x + 10

300

#10 Simplify using polynomial division:

(3x³ - x² - 40x + 48)/(3x - 4)

x² + x - 12

400

#15 Find the remainder when f(x) = x²⁰⁰¹ - 3x⁵³ + x² + 2 is divided by x+1

5