Mathematics
Grade10
Easy

Question

A rectangular patio has an area of 2x2 + 13x – 24 square feet. The patio is to be enlarged so that each dimension is 2 ft. greater than it was originally. What is the new area of the patio?

  1. 2x2 + 15x – 10
  2. 2x2 - 20x – 24
  3. x2 + 19x – 10
  4. 2x2 + 19x – 10

Hint:

Quadratic polynomial is a polynomial in which the highest degree monomial is of the second degree.

The correct answer is: 2x2 + 19x – 10


    2x2 + 13x – 24
    a = 2, b = 13, c = -24
    ac = -48
    Factors of -48 are 16 and -3.
    16 + (-3) = 13
    2x2 + 16x – 3x – 24 = 2x(x + 8) – 3(x + 8) = (2x – 3)(x + 8)
    The dimensions of the patio are 2x – 3 ft. by x + 8 ft.
    New dimensions are:
    2x – 3 + 2 = 2x – 1 ft.
    And x+8+2 = x + 10 ft.
    So, new area  = (x+10)(2x-1) = 2x² +19x -10.
    Hence, the correct option is D.

    Area of a rectangle = length × breadth sq. units.

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