A farmer's rectangular field has an area in which can be expressed as the trinomial x2 + 2x + 1. In terms of x, what are the dimensions of the field?

Because the formula for the area of a rectangle is A = length times width, ?nd out the two factors of x² + 2x + 1 to get the dimensions. First check to see if there is a general factor in each of the terms or if it is the difference among two perfect squares, and it is neither of these. The further step would be to factor the trinomial within two binomials. To do this, you will be doing techniques that resemble FOIL backwards (First terms of each binomial multiplied, Outer terms within each multiplied, inner terms of each multiplied, and Last term of each binomial multiplied.) First results in x², so the ?rst terms must be: (x  )(x ); Outer added to the Inner combines to 2x, and the Last is 1, so you required to ?nd two numbers in which add to +2 and multiply to +1. These two numbers would have to be +1 and +1: (x + 1)(x + 1). Because the factors of the trinomial are the similar, this is an example of a perfect square trinomial, meaning that the farmer's rectangular ?eld was more speci?cally, a square ?eld. To check to make sure these are the factors, multiply them through using FOIL (First terms of each binomial multiplied, Outer terms in each multiplied, Inner terms of every multiplied, and Last term of each binomial multiplied; (x • x) + (1 • x) + (1 • x) + (1 • 1); multiply within each term: x² + 1x + 1x + 1; combine such as terms: x² + 2x + 1.