# The area of a rectangle is found by multiplying the length by the width: A = lw. A certain rectangle has an area of x2 + 7x + 12. Factor the trinomial to find the length and width of the rectangle. In the form of a paragraph, describe the process necessary to factor the area of the rectangle into terms of its length and width.

## hint:

3+4 = 7

3*4 = 12

## To factor the trinomial x^2 + 7x + 12 into terms of the length and width of the rectangle, we need to find two binomials that, when multiplied together, give us the given trinomial.

First, we look for two numbers, let's call them a and b, whose sum is 7 and whose product is 12. To do this, we need to find the two numbers that satisfy the equation (a + b) = 7 and ab = 12.

By trial and error, we find that the numbers 3 and 4 meet these conditions. Therefore, we can rewrite the trinomial as (x + 3)(x + 4).

Now, as per the formula for the area of a rectangle, the length (l) is represented by (x + 3) and the width (w) is represented by (x + 4).

So, the factorized form of the trinomial x^2 + 7x + 12 is (x + 3)(x + 4), which represents the length and width of the rectangle as (x + 3) and (x + 4) respectively.

## To factor the trinomial x^2 + 7x + 12 in order to find the length and width of the rectangle, we need to rewrite the trinomial as a product of two binomials. To do this, we look for two numbers that multiply together to give us 12 (the constant term) and add up to 7 (the coefficient of the x term). In this case, the numbers are 3 and 4. So, we can rewrite the trinomial as (x + 3)(x + 4).

Now, the length and width of the rectangle correspond to the binomial factors. In this case, the length would be (x + 3), and the width would be (x + 4).

To summarize, we factored the trinomial x^2 + 7x + 12 into (x + 3)(x + 4) to find the length (x + 3) and width (x + 4) of the rectangle.

## Use the given area to find the dimensions of the quadrilateral.

(3x-3)(2x+3)=91