Factor the trinomial to find a possible combination of dimentions that the rectangle could have:
[tex]x^2-3x-18[/tex]To factor the trinomial, remember that the following product of binomials is equal to:
[tex](x+a)(x+b)=x^2+(a+b)x+ab[/tex]Then, we need to find two numbers a and b such that their product is equal to the constant term -18 and their sum is equal to the linear coefficient -3.
Since the product is negative, one number is negative and the other is positive.
Since the sum is negative, the greatest number is negative.
Two numbers whose difference is 3 and whose product is 18 are 6 and 3.
Notice that:
[tex]\begin{gathered} -6+3=-3 \\ (-6)(3)=-18 \end{gathered}[/tex]Then:
[tex]x^2-3x-18=(x-6)(x+3)[/tex]Therefore, the dimensions of the rectangle, are:
[tex](x-6)\text{ and }(x+3)[/tex]