a flower garden is 4 feet longer than its width. write a polynominal that represents the area of the garden

Question

Draw a picture

Answer 1

  ↑  w   
                        ←       l  = w + 4      →    

    A =     l       · w  
               ↓             
    A = (w + 4) · w , let's open parentheses by using distributive property of multiplication
    A = w² + 4w

 

Answer 2

Successfully solving a word problem requires some strategy.  A beginning to that strategy is to be able to determine what kind of a problem you're facing, and that will give you information about how to solve the problem.  This problem is an area problem -- the area of a geometric figure which can be determined by a formula.  The area of a rectangle is the product of the length and the width, shown in the formula "A=lw".  Our task is to write a polynomial that represents the area of that rectangle. 

A key piece to solving any word problem is the definition of your variables.  The better the definition, the better your understanding of the problem, and the better your ability to solve it.  This is something people who continue to struggle with word problems will skip over, or give short shrift to.  Complete sentences are useful.  Also, keep in mind that variables stand for numbers, and numbers in reality result from measurement, done in some kind of unit.  In this problem, the units are feet. 

'x' is a very popular variable to use, so let's define it like this:

"x is the number of feet the flower garden is wide"

I chose to assign x to the width of the garden, rather than the length, because the width is smaller, and that means that I can find the other unknown quantity by adding to it.  Assigning variables to the smallest quantity makes life a little easier.

So, if the width is represented by x, we need to represent the length, which the question tells us is four feet longer than the width.  Thus, the length will be x+4.

 

Now, with the formula "A=lw" we substitute the quantities we've come up with for the length and the width, giving us "A=(x+4)x".  Multiplying both the x and the 3 in the binomial, via the distributive law, gives the area as x^2 + 4x.  If you define your variable as I did above, this will be the answer to your question, and you can stop reading this now.  If you want to dig a little deeper, keep reading.

If we had defined x as the length, rather than the width, then the width would be three feet smaller than the length, and would be represented by "x-4".  In that case, when we multiply the length (x) by the width (x-4), we would get x(x-4), and the answer would be x^2 - 4x.  A different polynomial representing the same number.  This is why your answer is not only the polynomial, but, also, your definition of your variable -- so your instructor can determine which way you chose to go in that definition, and if you did so correctly.