Add and subtracting polynomials
(3r4 + 4r2) + (r4 - 6r2)
4r4 - 2r2
-3x2 ( 4x2 + 6x - 8 )
12x4 - 18x3 + 24x2
Mrs. Leland is cutting out squares for a geometry game. The last square has a side length 3 inches longer than the first square. Write an expression that could be used to find the area of the last square if the first square’s side measured x inches.
x2 + 6x + 9
Janice wants to put up a wallpaper border around a room that is 5 feet longer than its width. She calculates that she needs 50 feet of border. What is the length and the width of the room?
10 feet
( x - 2 ) ( x + 4 ) = 0
x = 2
x = -4
(8n + 7y - 2) + (4n + 8)
12n + 7y + 6
x( 5x + x2 )
x3 + 5x2
Kurt designs a square flower garden that has the same area as a rectangular one. The length of the rectangular garden is 10 feet longer than the side of the square garden. The width of the rectangular garden is 5 feet shorter than the side of the square. Find the length of the rectangular garden in feet.
20 feet
A circular driveway has an unknown radius of x feet. If the radius was increased by 5 feet, write an expression that would represent the new circumference.
(2x+10)pi
x = 7
x = -5
( -2x + 5 ) + (-4x2 + 6x + 9 )
-4x2 + 4x + 14
3y( -4x - 6x3 - 2y )
-18x3y - 12xy - 6y2
An irrigation system used on the west coast is made up of a long arm that rotates around a center point, making the path of a circle. The arm, which contains the sprinkler head, is 50 yards long. If a farmer wants to add x yards to the length of the irrigation arm, write the expression that gives the total area covered by the new irrigation system.
piX2 + 100piX + 2500pi
The length of a rectangle is three more than the width. The perimeter of the rectangle is 26 inches. What are the width and length of the rectangle.
Width: 5 in
Length: 8 in
2x2 - 6x = 0
x = 0
x = 3
(8x2 + 2x + 10) - ( 3x2 - 9x - 1 )
5x2 + 11x + 11
(3x - 1 )( 9x + 4 )
27x2 + 3x - 4
A rectangular parking lot has a small rectangular area in one corner that needs to be repaired. The
dimensions are shown in the drawing. What is the area of the parking lot that does NOT need repair?
89x2
A triangle has a perimeter of 12x² + 4x - 7 and two other side lengths of x² + 10 and 8x - 11. What is the length of the third side?
11x² -4x - 6
x2 + 6x + 8 = 0
x = -4
x = -2
( 8xy + x3 - 6 ) - ( -10xy + 7 - 2x3 + 5x2 )
3x3 - 5x + 18xy - 13
( 2x + 5 )( 3x2 + x + 2 )
6x3 + 17x2 + 9x + 10
An irregularly shaped lot is made up of two rectangular sections. Given the dimensions below, write a polynomial that shows how many square feet make up the lot.
7x2 + 16x + 8
Find the circumference of a circle with a radius of (2x-6).
4piX-12pi
y = 5x2 + 14x - 3
x = 1/5
x = -3