The area of a rectangular room is given by the trinomial x² + 3x - 28. What are the possible dimensions of the rectangle? Use factoring,
(x - 7) and (x + 4)
(x - 7) and (x - 4)
(x + 7) and (x + 4)
(x + 7) and (x - 4)

Solution:

Given area of a rectangular room is given as x² + 3x - 28

The dimensions of the room can be calculated by deriving its factors

f(x) = x² + 3x - 28

For finding factors, we can use quadratic equation

x = -b ± √(b² - 4ac) / 2a

Here a = 1; b = 3; c = -28

x = -3 ± √(3² - 4(1)(-28)) / 2(1)

x = -3 ±√(9 +112) / 2

x = -3 ±√(121) / 2

x = -3 ± 11 /2

x = -14/2 , 8/2

x = -7, 4

We need to write these in factor form (x - a) as (x - (-7) and (x - 4)

Hence the factors are (x + 7) and (x - 4)

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The area of a rectangular room is given by the trinomial x² + 3x - 28. What are the possible dimensions of the rectangle? Use factoring,

Summary:

The area of a rectangular room is given by the trinomial x² + 3x - 28, the possible dimensions of the rectangle are (x + 7) and (x - 4).