The area of a rectangular carpet is given by the trinomial 5x^2 - 3x - 14. What are the possible dimensions of the carpet? Use factoring.

Answer 1

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

First, multiply the coefficient of the x^2 term (5) and the constant term (-14) to get -70.

Next, find two numbers that multiply to -70 and add up to the coefficient of the x term (-3). The numbers are -10 and 7.

Now, split the middle term -3x into -10x + 7x:

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

Factor by grouping:

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

(x - 2)(5x + 7)

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