Polynomials

Characteristics of Polynomials

100

The sum or difference of two or more monomials

What is a polynomial

200

The highest exponent in a polynomial

What is the degree of a polynomial

300

A polynomial with three terms.

What is a trinomial

400

The only way to add or subtract polynomials is to combine these

What are like terms. Same variable, same exponent!

500

The property needed to multiply polynomials.

What is the Distributive Property?

Adding Polynomials

100

Find the sum: (3x+4)+(7x+2)

What is 10x+6

200

Find the sum: (2x²+8x+4)+(x²-3x-2)

What is 3x²+5x+2

300

Find the sum: (4x²+5x+1)+(-2x²+7)

What is 2x²+5x+8

400

Find the sum: (12x³+4x²+7x+8)+(2x³-5x²+2x-10)

What is 14x³-x²+9x-2

500

Find the sum: (5x⁴+3x³-x²+2x+4)+(x⁴-6x³-2x²+6x+7)

What is 6x⁴-3x³-3x²+8x+11

Subtracting Polynomials

100

Find the difference: (6x²+2x+4)-(3x²+x+2)

What is 3x²+x+2

200

Find the difference: (5x²-4x-7)-(2x-9)

What is 5x²-6x+2

300

Subtract 5x² + 2x − 11 from x²  + 8x − 7. Express the result as a trinomial.

What is -4x² + 6x + 4

400

When (x − 4)²  is subtracted from 5x², the result is?

What is 4x² - 8x+16

500

Find the difference of the sum of (2x³-3x²-3x+5) and (x³+2x²-4x+2) and the product of (2x² - 3x) and 

(2x +4)   

What is -x³-3x²+5x+7

Multiplying/Dividing Polynomials

100

Find the product: (x+2)(x+4)

What is x²+6x+8

200

Find the product: (3x+3)(x-2)

What is 3x² -3x-6

300

Find the answer: 3(2x-6)²

What is 12x²-72x+108

400

Find the quotient of: (4x⁵+ 2x⁴ - 6x³ - 12) / (2x³)

What is 2x²+x -3 - 6/x³ 

500

Find the quotient: (21a²b³c⁵ - 49a³b + 21b⁴c³) / 7a³b²c³

What is (3bc²) /a - 7/(bc³) + (3b²)/a³ 

Word Problems with Polynomials

100

Fred is given a rectangular piece of paper. If the length of Fred's piece of paper is represented by

2x − 6 and the width is represented by 3x − 5, then the paper has a total area of?

What is 6x² - 28x + 30

200

A photo is surrounded by a frame with a border which is 7 inches wide. If the photo has a length that is 6 inches longer than the width,

• Find the area of the photograph, written as a polynomial, in terms of x.

What is x²+6x?

300

A photo is surrounded by a frame with a border which is 7 inches wide. If the photo has a length that is 6 inches longer than the width,

• Find the total area, written as a polynomial, in terms of x.

What is w² + 34w + 280?

400

A photo is surrounded by a frame with a border which is 7 inches wide. If the photo has a length that is 6 inches longer than the width,

• Find the dimensions of the photo, if the area along one of the widths is 133 square inches.

What are width = 5 inches and length = 11 inches?

500

A photo is surrounded by a frame with a border which is 7 inches wide. If the photo has a length that is 6 inches longer than the width,

• Find the dimensions of the photo and the frame's dimensions, if the area along one of the lengths is 210 square inches.

What are width = 10 inches and length = 16       inches for the photo, and width = 24 inches and length = 30 inches for the frame?