Write trinomial expression from word porblem

dbush

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I'm trying to help my son with his homework and I have no idea where to go with this one. Here goes...

Janelle wants to enlarge a square graph that she has made so that the sides of the graph will be 1 inch more than twice the original side s. What trinomial expression represents the area of the enlarged graph?

Ok -so a trinomial is x2 + bx + c = 0

Is the answer:

x2 + 2x + 1 = 0
 
Thanks for the advice on both counts. I agree with your assessment, but we are dealing with some unique circumstances. For now, I am taking the role of checking his homework because the teacher does not go over homework in class. So, he never really knows if he has done the problems correctly until he is presented with a test, then it's too late. I do not help him do his homework unless he is totally stumped. We compare answers and discuss where a mistake was made (mine or his) if our answers differ. The problem is that sometimes I am the one so stumped that I do not know where to start, which is usually when I land here. I don't want to assume that his answer is correct unless I can work it out for myself.


Sorry for the novel but I thought I should explain. I appreciate the tremendous help all of you have been.
 
Thanks for the advice on both counts. I agree with your assessment, but we are dealing with some unique circumstances. For now, I am taking the role of checking his homework because the teacher does not go over homework in class. So, he never really knows if he has done the problems correctly until he is presented with a test, then it's too late. I do not help him do his homework unless he is totally stumped. We compare answers and discuss where a mistake was made (mine or his) if our answers differ. The problem is that sometimes I am the one so stumped that I do not know where to start, which is usually when I land here. I don't want to assume that his answer is correct unless I can work it out for myself.


Sorry for the novel but I thought I should explain. I appreciate the tremendous help all of you have been.

You're GIVEN that the length of a side of the original square is "s" units.

You're told that the new square will have sides that are "one inch more than twice the side of the original square".

s = side of original square
2s = "twice the side of the original square"
2s + 1 = "one inch more than twice the side of the original square"

Now...to find the area of ANY rectangle, you multiply length X width.

A square is a special rectangle where the length and the width are the same. And the square in your problem has sides of 2s + 1, so the "length" is 2s + 1, and the "width" is 2s + 1.

So, the area of the new square is (2s + 1)(2s + 1)

This is not a trinomial YET, but it will be if you do the multiplication....your child should (I hope) be able to do that.
 
I'm trying to help my son with his homework and I have no idea where to go with this one. Here goes...

Janelle wants to enlarge a square graph that she has made so that the sides of the graph will be 1 inch more than twice the original side s. What trinomial expression represents the area of the enlarged graph?

Ok -so a trinomial is x2 + bx + c = 0

Is the answer:

x2 + 2x + 1 = 0

That is a general expression that describes quadratic equations (although incomplete, the complete one says \(\displaystyle ax^2+bx+c\)).

Trinomial is a name for any polynomial with three terms (for example \(\displaystyle a+3c+2b\), where \(\displaystyle a\), \(\displaystyle 3c\) and \(\displaystyle 2b\) are terms).

This problem requires your son to know a formula that is called a "square of a binomial". So, as Jeff implied, you have the new length of a graph and you need a trinomial expression that represents the area of enlarged graph.

Text of the problem reveals that the new, enlarged graph has the length of its side, that is one inch longer than TWICE the old size, \(\displaystyle s\). So, the new side has a length of \(\displaystyle 2s+1\).

The area of the square is the length of it's side multiplied by itself, in other words squared. So, the new area is \(\displaystyle (2s+1)^2\). In order to square this binomial, you need to use the square of a binomial formula. The result of squaring a binomial is a trinomial, so that will be your answer.

Square of a binomial:


\(\displaystyle (a+b)^2=a^2+2ab+b^2\)

\(\displaystyle (a-b)^2=a^2-2ab+b^2\)

I will leave it to you to complete the answer to this problem.

By the way, Jeff is completely right. Getting the answer without the work invested in its obtaining is counterproductive. It would be better if you introduced your son to this forum so he can seek help on his own. Getting the answer "on the plate" is not the point, investing time into getting it (even if you don't succeed on your own) is what it's all about.
 
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Makes perfect sense and seems so simple now. Duh! Thanks to all!
 
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