Chapter 4 Test Review: Products and Factors of Polynomials

Polynomials 101

100

What is another name for a number?

Ex: 6

Constant

200

Identify the coefficient of the following monomial: 

-xy^3

-1

300

Identify the degree of the following term: 

-4x^3yz^2

6

400

Identify the degree of the following polynomial: 

4x^3 + 2x^2y^3 - 6x^2

5

500

Identify the 3 basic forms of a monomial

A constant, a variable, or a product of these two

Polynomial Jewelry

100

Add: (x^2 + 4x - 2) + (6x^2 - 2x + 8)

7x^2 + 2x + 6

200

T/F: The constant -9 is considered a polynomial.

True

300

Simplify: (3x)(-4x^5)

-12x^6

400

Simplify: (-2x^3y^4)^3

-8x^9y^12

500

Simplify: x^(m-1)*x*x^m

x^2m

Aluminum Foil

100

Simplify: (x - 1)(x + 2)

x^2 + x - 2

200

T/F: (x + y)^2 = x^2 + y^2

False

300

Simplify: (cat + dog)(cat - dog)

cat^2 - dog^2

400

T/F: (x - y)^3 = x^3 - y^3

False

500

(x +y)(x - y) are known by what name?

Conjugates

Factoring in Heaven

100

Factor: x^2 - 9x + 8

(x-8)(x-1)

200

What is always the first step in factoring?

To factor out the GCF

300

Complete the Formula for the Difference of Two Squares:   a^2 - b^2 = ?

(a+b)(a-b)

400

Complete for formula for the sum of two cubes: 

a^3 + b^3 = ?

(a + b)(a^2 - ab + b^3)

500

T/F: Every polynomial can be factored no matter how complicated it is.

False: Some polynomials are Prime which means they cannot be factored.

I've Got a Major Problem

100

Solve: (x + 4)(x - 5) = 0

x = -4, 5

200

Solve: (2z - 1)(3z + 5) = 0

x = 1/2, -5/3

300

T/F: The solution to some polynomial inequalities can be the set of all real numbers.

True

400

Solve: x(x - 1)(2x - 9) = 0

x = 0, 1, 9/2

500

Consider the following Polynomial Equation: 

x^5 + 4x2 - 2 = 0. 

Assuming all possible solutions are real, what is the total number of real roots that we will have?

5