Factoring Algebraic Expressions Word Problems

A rectangle has an area of 2x² – 19x +45 ft². What are the dimensions of the rectangle?  

• (2x - 9)(x - 5)
• (2x + 9)(x + 5)
• (2x - 5)(x - 9)
• (2x - 5)(x + 9)

A rectangle has an area of 4x² +19x + 12 and a length of (x + 4). What is the width?

• 4x - 3
• 4x + 3
• 2x + 6
• 2x + 3

A rectangle has an area of 25x² - 81, what are the length and width of the rectangle?

• (5x - 9) & (5x + 9)

• (5x - 9) & (5x - 9)

• (5x + 9) & (5x + 9)

• There is no way for us to know.

A rectangle has an area of k² -2k - 24, what is the length & width of the rectangle?

• (k+4) & (k-6)

• (k+4) & (k+6)

• (k+6) & (k-1)

• (k-4) & (k+6)

Factor Completely.  
8x³ - 18x

• 2x(4x²-9)                                    
• (4x²+3)(2x-3)
• 2x(2x+3)(2x-3)
• PRIME

Find the area of the rectangle.

• 9x² - 2x
• 9x² - 2
• 10x - 2
• 20x - 4 

Find the perimeter of the rectangle.

• 5x + 5
• 10x + 10
• 20x + 4
• 20x

The area of a rectangle is (6x²+7x+2) square inches and the length is (3x+2) inches. Which expression represents the rectangle's width?

• (2x+2) inches

• (2x-2) inches

• (2x+1) inches

• (2x-1) inches

A square has an area of 25x²+20x+4 square feet. Find the length of the square.
HINT: Squares have equal sides

• (x+2) meters
• (x-2) meters
• (5x+2) meters
• (5x-2) meters

If the length of a rectangle is (x + 7) inches and the width is (3x+2) inches. Which expression represents the rectangle's area?
HINT: Area = width * length 

• 3x² + 23x + 14 square inches
• 4x² + 21x + 14 square inches
• 4x +9 square inches
• 3x² + 12x + 9 square inches