To find the area of the rectangle, we can use the formula
Write two
binomials that could represent the length and width of the rectangle.
Problem 1 :
4x² - 7x – 2
Solution :
Area of rectangle = length × width
Area = 4x² - 7x – 2
= 4x² - 8x + x – 2
= 4x(x - 2) + 1(x - 2)
= (4x + 1) (x - 2)
So, the length of rectangle is (4x + 1), and width is (x - 2).
Problem 2 :
16x² - 25
Solution :
Area of rectangle = length × width
Area = 16x² - 25
(a² - b²) = (a + b) (a - b)
= (4x + 5) (4x - 5)
So, the length of rectangle is (4x + 5), and width is (4x - 5).
Problem 3 :
9x² - 6x + 1
Solution :
Area of rectangle = length × width
Area = 9x² - 6x + 1
= 9x² - 3x – 3x + 1
= 3x(3x - 1) – 1(3x - 1)
= (3x - 1) (3x - 1)
So, the length of rectangle is (3x - 1) and width is (3x - 1).
Problem 4 :
3x² + 5x – 2
Solution :
Area of rectangle = length × width
Area = 3x² + 5x – 2
= 3x² + 6x – x – 2
= 3x(x + 2) – 1(x + 2)
= (3x - 1) (x + 2)
So, the length of rectangle is (3x - 1) and width is (x + 2).
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