Algebra I Chapter 7 Review

Terms

1

Which of the following describes a number whose only factors are 1 and itself?

(a) Prime

(b) Composite

(a) Prime

2

Which of the following is a perfect square trinomial?

(a) x² - 16

(b) x² + 3x + 20

(c) x² + 5x + 25

(c) x² + 5x + 25

3

When two binomials have the same terms but opposite signs, they can be described using which of the following terms?

(a) Inverses

(b) Conjugates

(c) Similar

(d) Prime

(b) Conjugates

4

According to the fundamental theorem of arithmetic, every _________ number can be rewritten as a sum of _______ numbers.

(a) Prime, Composite

(b) Even, Odd

(c) Radical, Exponent

(d) Composite, Prime

(d) Composite, Prime

5

Which of the following allows for each factor of a factored quadratic equation to be set equal to zero?

(a) Fundamental Theorem of Arithmetic

(b) Zero Factor Property

(c) Zero Property

(d) Factoring Property

(b) Zero Factor Property

Factoring (GCF)

1

Factor the following polynomial: 15x⁵ + 20x³.

5x³(3x² + 4)

2

Factor the following polynomial: 25x³y + 40x²y² - 5xy³.

5xy(5x² + 8xy - y²)

3

Factor the following polynomial: a⁴b + a³b² - ab³.

ab(a³ + a²b - b²)

4

Factor the following polynomial: 12r²st² - 3rst - 6rs²t².

3rst(4rt - 1 - 2st)

5

Factor the following polynomial: 72x⁵y² - 28x³y⁴ + 60x²y³.

4x²y²(18x³ - 7xy² + 15y)

Factoring (Special Forms)

1

When you encounter the special case known as the difference between two squares, you factor it as which of the following?

(a) Prime

(b) Conjugates

(c) Binomial Squared

(b) Conjugates

2

Factor the following polynomial: x² - 9.

(x + 3)(x - 3)

3

Factor the following polynomial: x² + 64.

Prime (Sum of Two Squares)

4

Factor the following polynomial: x² + 12x + 36.

(x + 6)²

5

Factor the following polynomial: x² - 18x + 81

(x - 9)²

Factoring (General)

1

Factor the following polynomial: x² + 3x + 2.

(x + 2)(x + 1)

2

Factor the following polynomial: x² - 5x - 50.

(x - 10)(x + 5)

3

Factor the following polynomial: 2x² + 5x + 2.

(2x + 1)(x + 2)

4

Factor the following polynomial: 3x² + 2x - 8.

(3x - 4)(x + 2)

5

Factor the following polynomial: 3x² + 8x - 35.

(3x - 7)(x + 5)

Quadratic, Linear, and Constant Terms

1

Identify the constant term in the following polynomial: x² + 4x + 4.

Constant Term = 4

2

Identify the quadratic term in the following polynomial: x² -2x - 24.

Quadratic Term = x​²​​​​​​​

3

Identify the linear term in the following polynomial: x² - 49.

Linear Term = None

4

In a polynomial which of the following terms has an exponent of 1?

(a) Quadratic

(b) Linear

(c) Constant

(b) Linear

5

In a polynomial which of the following terms has an exponent of 0?

(a) Quadratic

(b) Linear

(c) Constant

(c) Constant