Question

MEDAL AND FAN WILL BE GIVEN JUST HELP!

Just help me with this.

Part A: The area of a square is (9x2 - 12x + 4) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work.

Part B: The area of a rectangle is (25x2 - 16y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work.

Part C: The volume of a rectangular box is (x3 - 7x2 - 9x + 63) cubic units. Determine the dimensions of the rectangular box by factoring the volume expression completely

Answer 1

@triciaal @Directrix @mathmale @mathstudent55 @zepdrix

Answer 2

@ParthKohli @pooja195 @Nnesha @jagr2713 @ShadowLegendX @inkyvoyd @Awolflover1 @sweetburger

Answer 3

Im gonna ask this in geometry. If you respond, tag me so that I'm alerted

Answer 4

if you factor out the polynomial representing the area of the rectangle, you'll end up with to binomials multiplied, which represent the product of two sides.
so, you have an area represented by: \(A= 9x^2-12x+4\) and factoring this out will yield the product of two binomials.

Answer 5

@Owlcoffee Small words please

Answer 6

@Owlcoffee Wait, now I get it

Answer 7

Factor out \[A= 9x^2-12x+4\]

Answer 8

Okay, so A is simple. All I have to do is factor 9x2 -12x + 4, correct?

Answer 9

yes.

Answer 10

What does part b mean by dimensions of the rectangle?

Answer 11

@Owlcoffee ?

Answer 12

Did you want to do the first one and factor it out?

Answer 13

If so then we know it is a square so the sides must be the same.

Answer 14

@MedicalDoctor I'm kinda in a rush right now. I have to step out for like 20 - 30 minutes right now. So all I wanna know is how to solve the questions

Answer 15

The second one is the same.
The dimensions of a rectangle is the product of it's sides: \(A=b \times h\)
so it's the same as in the first exercise, factor it out and the dimensions will be evident.

Answer 16

Okay, I have to leave. Can you just explain the process for completing Parts B and C?

Answer 17

Since it is square what would that tell us about the factors?

Answer 18

I'll ask you any questions I have once I'm back, Ill tag you

Answer 19

Just explain how to solve b and c plz, thx

Answer 20

g2g, Be back in about 30 minutes or a bit longer, bye!

Answer 21

When you multiply them together to get the area, it has to be a perfect square so this is going to be a perfect squared trinomial.

Answer 22

In the case of a perfect square, all we need to do is find the square roots of the first and last terms so the question is now, what is the square roots of 9x² and 4.

Answer 23

So our square root of 9x^2 is 3. Therefore the 3x gives us the first part in the factor.

Answer 24

The other one is for the 4. We need the root of 4.

Answer 25

Our square root of 4 is 2 because a square root is a number that multiplied by itself equals the goal number. So this is our second number. Therefore it is 3x and 2. Did you have any questions so far?

Answer 26

Part B is a new "trick",
I don't know if we've gone over it at all in the last few days.
`The product of conjugates produces the difference of squares`.

Here is the trick: \(\large\rm a^2-b^2=(a-b)(a+b)\)
On the left side, difference of squares, subtraction of squared numbers.
On the right side, these are called conjugates, they look the same, but with a different sign between them.

So you need to rewrite your \(\rm 25x^2 - 16y^2\) as a square minus a square.
\(\rm 25=5^2\) and \(\rm 16=4^2\)

therefore we have \(\rm 5^2x^2-4^2y^2\)
which we can write as \(\rm (5x)^2-(4y)^2\)

Good, now it's written as a square minus a square,
so you can apply the trick :)

Answer 27

There is one more The sign in between 3x and 2 is either going to be a + or - That's easy to find with perfect square trinomials, though. It's negative because of the -12

Answer 28

So we end up with 3x - 2.

Answer 29

Part C is a mixture of the rules you've learned so far.
You'll start to factor it by grouping,
then you'll have to apply your difference of squares trick.

\[\large\rm x^3-7x^2-9x+63\]

Answer 30

@zepdrix Wait, what do I have to do for Part B and C?

@medicaldoctor

Answer 31

@Owlcoffee Im confused on Part B and C, can you help?

Answer 32

(25x2 - 16y2) = (10x2 + 15x2 - 8y2 - 8y2)

Group:

(10x2 + 15x2) - (8y2 - 8y2)

Common factor:

GCF for Binomial 1: 5x2

GCF for Binomial 2: 8y2

Divide out:

5x2(2 + 3) - 8y2(-1 - 1)

Join together:

(5x2 - 8y2)(2 + 3) (-1 - 1)

@nincompoop HELP!