Katie's school has a rectangular courtyard whose area can be expressed as 3x² - 7x + 2. Which of the following could be the dimensions of the courtyard in terms of x?

Since the trinomial does not have a coef?cient of one on its highest exponent term, the simplest way to ?nd out the answer to this problem is to use the distributive property.  First, by using the original trinomial,  identify the sum and product  through looking at the terms when the trinomial  is in descending order (highest exponent ?rst): 3x² - 7x  +   2.The  sum is the middle term, in this case,    7x.The product  is the product  of the ?rst and last terms, in this case, (3x²)(2) =   6x². Now, identify two quantities whose sum is -7x and product  is 6x², namely -6x and -x. Rewrite the original trinomial  using these two terms to replace the middle term in any order: 3x² -6x - x + 2. Now factor by grouping  by taking a common factor out of each pair of terms.The common factor of 3x2 and -6x is 3x and the common factor of -x and 2 is -1.Thus, 3x² - 6x - x + 2 becomes 3x(x - 2) - 1(x - 2). (Remember that if this expression was multiplied back out and simpli?ed, it would correctly yield the original polynomial.)Presently, this two-term expression has a common factor of (x - 2) which can be factored out of each term using the distributive property:  3x(x - 2) - 1(x - 2) becomes (x - 2)(3x -1).The  dimensions of the courtyard are (x - 2) and (3x - 1).