Question

part A) the area of a square is (25x^2 - 20x + 4) square units. determine the length of each side of the square by factoring the area expression completely.

Part B) the area of a rectangle is (49x^2 - 36y^2) square units. Determine the dimensios of the rectangle by factoring the area completely.

part C) the volume of a rectangular box is (x^2 + 2x^2 - 9x - 18) cubic units. determine the dimensions of the rectangular box by factoring the volume expression completely.

PLEASE HELP ME??

Answer 1

@hero @mathmale

Answer 2

@whpalmer4 can you help me?

Answer 3

I'd like to start by asking you some questions.
1) In (A), above, what is the shape of the given area?
2) Given the length of one side of a square, what is the AREA of the square?
3) Given the area of a square, how would you find the length of one side of the square?

Answer 4

@mathmale

1.) its a square
2) it desnt give me the length.

the answer i got for A IS (5X-2)^2

Answer 5

So, stromberg: You know this figure is a square, and you are given the area. How would you yourself figure out the length of one side?

Suppose I gave you another square and told you that the area were 49. How would you find the length of one side of that square?

Answer 6

What my friend @mathmale was asking for in his second question was simply the relationship between side length and area. \[A=f(s)\]where \(s\) is side length and \(f(s)\) is some function of \(s\). What is the formula for the area of a square?

Answer 7

Oops, and now I see he's here as well. I think I'll get a few more minutes of sleep :-)

Answer 8

Ooops! We have to finish what we start, don't we? :)

Answer 9

A hint for @stromberg1: suppose the area of a square is A = 49, and we know that the area of a square is simply the square of the length of one of its sides. What's the length of a side of this particular square? Hint: #2: think "square root."

Answer 10

i honestly have no clue... i ask my teacher for help and she gives me a long lecture about how i should know this @mathmale

Answer 11

Thank you for your response:

1.) its a square
2) it desnt give me the length.

the answer i got for A IS (5X-2)^2

1. True. We do have a square.
2. True; you are not given the length of a side of this square; you are asked to determine that length yourself. The question is: HOW?

3. Please multiply out (5x-2)^2 = (5x-2)(5x-2). Then compare your result with the given area, 25x^2 - 20x + 4. What could you conclude?

Answer 12

I'm trying to ask questions that might lead you towards understanding this material better. Sorry it's taking so long.

You are correct: You do have a square here.
You're given the area of the square and probably have seen before that the aera of a square is A = s^2, where s is the length of one side of the square.

Suppose we wanted to obtain the length of one side. All we'd need to do would be to find the square root of both sides of this equation.

Can you do that?

Answer 13

\[If~A=s^2,~then~\sqrt{s^2}=s=\sqrt{A}\] which gives you the answer you want.

If A =49, what is the length of one side of the square?

Answer 14

no.. i cant do it. im dumb. im doomed @mathmale

Answer 15

You are neither dumb nor doomed! This material is just unfamiliar. With practice, you'll get it.

If the area of a square is 49, the length of one side is s=Sqrt(49), or +7:\[s=\sqrt{49}=+7\]

Answer 16

So, if the area of another square is 25x^2 - 20x + 4, the length of one side is
s=Sqrt(25x^2 - 20x + 4), or\[s=\sqrt{25x^2 - 20x + 4}=\sqrt{(5x-2)^2}=?\]

Answer 17

5x-2?

Answer 18

@mathmale

Answer 19

Yes! That's it. You've successfully found the length of one side of the given square. Congrats!

Answer 20

yay!! thank you

Answer 21

Nice work! Keep it up! Thanks for your persistence and patience.

Answer 22

i think i can figure out b myself. but do you have time to help me with c? @mathmale

Answer 23

\[x^2 + 2x^2 - 9x - 18\]
I am skeptical that the expression you have given us for C is correct. Can you check it?

I am skeptical because a) it doesn't factor and b) the volume of a box should have dimensions [length]\(^3\) and this does not, unless we assume that one side was represented by a number rather than an expression involving \(x\).

Answer 24

I think it more likely to be \[x^3 + 2x^2 - 9x - 18\]which suffers from neither of those impediments.

I would suggest factoring this by grouping. I'll do an example with a different problem to show you how it is done.

\[x^3+3x^2-4x-12\]We're going to start by writing this as two "groups", enclosing each pair of terms in parentheses:
\[(x^3+3x^2) + (-4x-12)\]Notice that I've inserted a "+" in front of the second group, even though the terms have "-" signs in front of them. This is to eliminate a common source of error, and does not change the value of the expression.

Now we factor each pair of terms:
\[x^2(x+3) +(-4)(x+3)\]Hey, look at that — both expressions have \((x+3)\) as a common factor! We will factor it out:\[(x+3)(x^2+(-4))\]or\[(x+3)(x^2-4)\]
Whenever you see something that has a squared variable and a negative sign, such as \((x^2-4)\), you should start thinking "could this be a difference of squares?"

You can factor a difference of squares like this:\[a^2-b^2 = (a+b)(a-b)\]
Comparing with \(x^2-4\), we can see that is a difference of squares with \(a=x\) and \(b=2\), so \[x^2-4 = (x-2)(x+2)\]and our fully-factored expression is\[x^3+3x^2-4x-12=(x+3)(x-2)(x+2)\]

Now you should be able to do the same process with the polynomial from part C.

Answer 25

You can check your final answer by multiplying it out and verifying that you get the same polynomial you factored.