The area of a rectangular carpet is given by the trinomial 5x - 3x - 14 what are the possible dimensions of the carpet using factoring

Answer 1

To find the possible dimensions of the carpet, we need to factor the trinomial 5x^2 - 3x - 14.

First, we need to find two numbers that multiply to -70 (product of the coefficients of x^2 and the constant term) and add up to -3 (coefficient of x). The two numbers are -10 and 7.

So, we can rewrite the trinomial as:

5x^2 - 10x + 7x - 14

Now, we can factor by grouping:

5x(x - 2) + 7(x - 2)

Factor out the common factor (x - 2):

(x - 2)(5x + 7)

So, the possible dimensions of the carpet are x - 2 and 5x + 7.