MAT 097

Factoring GCF and Trinomials

100

What is the Greatest Common Factor of 12 and 18?

6

200

What is the Greatest Common Factor of 6x⁵ and 4x³

2x³

300

x² + 13x + 30

(x + 3) (x + 10)

400

x² - 11x +24

(x - 3) (x - 8)

500

2x⁴ - 26x³ + 84x²

2x² (x - 6) (x - 7)

Systems of Equations

100

Is (-3, 1) a solution of the system: 

x - y = -4

2x + 10y = 4

Yes

200

Solve the system:

3x - y = 4

6x - 2y = 4

8 ≠ 4

No Solution

300

Solve the system:

x + y = 7

x - y = 9

x = 8

y = -1

400

Solve the system:

6x - 3y = -3

4x + 5y = -9

x = -1

y = -1

500

Solve the system of equations:

x = 3y -1

2x - 6y = -2

y = 1/3x + 1/3

y = 1/3x + 1/3

Infinite solutions

Exponents

100

(x⁴) (x⁵)

x⁹

200

(-7x¹⁰y⁷z³)⁰

1

300

(-5x³y²z⁴)²

25x⁶y⁴z⁸

400

(2x⁴/3y⁵)⁴

16x¹⁶/81y²⁰

500

-32(x³y^-3)^-5/8x^-5y^-6

-4y²¹/x¹⁰

Quadratic Equations

100

x² - 3x - 18 = 0

x = -3

x = 6

200

9x² - 24x = -16

x = 4/3

300

x - 12x - 5 = -6x + 2

x = -1

x = 7

400

3x³ - 12x = 0

x = 0

x = -2

x = 2

500

The length of a rectangular garden is 5 feet more than its width. The area of the garden is 176 square feet. Find the length and width of the garden.

Width: x = 11

Length: x+5 = 16

Random

100

(4x² - 9) - (-5x² + 6x -2)

9x² - 6x - 7

200

(8a - 3)²

64a² - 48a + 9

300

25x² - 80x + 64

(5x - 8)(5x - 8)

400

-7x² + 2x +1

A) What is the degree of the polynomial?

B) What is/are the coefficient(s)?

C) What is the constant?

D) How many terms are there?

E) Is this polynomial a monomial, binomial, or trinomial?

A) 2

B) -7, 2, 1

C) 1

D) 3

E) Trinomial

500

The square of a number is 12 more than the number. Find all such numbers.

x = 4

x = -3