FACTORING POLYNOMIAL TO DETERMINE THE DIMENSION OF RECTANGLE

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).