Polynomials and Factoring

Word Problems

100

Write a binomial whose terms have a GCF of 3x.

Sample answer: 6x^2 + 3x

200

A punter can kick a football with an initial velocity of 48 feet per second. How many seconds will it take for the ball to return to the ground? Use the formula h=vx -16x^2 to solve the problem.

3 seconds

300

The height h (in feet) above the water of a cliff diver is modeled by h = −16x^2 + 8x + 80, where x is the time (in seconds). How long is the diver in the air?

2.5 seconds

400

The length of a Charlotte, North Carolina, conservatory garden is 20 yards greater than its width. The area is 300 square yards. What are the dimensions?

Width is 10 yards and length is 30 yards

500

A box in the shape of a rectangular prism has a volume of 180 cubic inches. The dimensions of the box in terms of its height are the following: (x+9), (x - 4), and x inches. Find the length, width, and height of the box.

The length is 15 inches, the width is 2 inches, and the height is 6 inches.

Multiplying Polynomials/Special Products of Polynomials

100

Multiply (2x)(8 - x - 3x²)

What is 16x - 2x² - 6x³

200

Multiply (3t + 5)(t - 3)

What is 3t² - 4t - 15

300

(y - 4)(y + 4)

What is y² - 16

400

(2x + 10)(5x + 2)²

What is 50x³ + 290x² +280x + 40

500

Multiply (3n + 4m)²

What is 9n² + 24mn + 16m²

Factoring ax^2+bx+c

100

Factor y² + 5y - 14

What is (y + 7)(y - 2)

200

Factor x² - 3x - 88

What is (x + 8)(x - 11)

300

Solve t² + 23t + 90

What is (t + 18)(t + 5) t= -18 and -5

400

Factor 14x² + 36x - 18

What is 2(7x - 3)(x + 3)

500

Factor 18x² + 57x - 108

What is 3(3x-4)(2x+9)

Factoring Special Products/Factoring Using the Distributive Property

100

Factor 49x² - 36

What is (7x - 6)(7x + 6)

200

Factor 4x² + 32x + 64

What is (2x+8)²

300

Factor 72 - 50y²

What is 2(6 + 5y)(6 - 5y)?

400

Factor 2n³ - 4n² - 30n

What is 2n(n + 3)(n - 5)

500

-y⁴ - 3y³ - 2y² - 6y

What is -y(y² + 2)(y + 3)?

Anything Goes

100

Expand 3(x + 12)(x + 7)

3² + 57x +84

200

Multiply (5x + 5)(5x - 5)

What is 25x² - 25

300

Multipy (x - 11)²

What is x² - 22x + 121

400

Factor x² + 4x - 7

What is NOT Factorable :-)

500

Factor 48x³ - 75x

What is 3x(4x - 5)(4x + 5)