Question

Could someone help me with this assignment? I'm struggling.

Answer 1

with wut

Answer 2

I have to find the linear factors of the polynomial

Answer 3

Eh I'm confused, can you show me the steps on how to find that?

Answer 4

uhmm ..i go to chek..its worn ...

Answer 5

worng cuz when u multiply it..u wont get it

Answer 6

I see, well I'd be very grateful if someone could go through the steps with me in order to solve it.

Answer 7

Use synthetic division to divide the polynomial by (x-1). This will help you find the other factors.

Answer 8

So 2x^3+9x^2+4x-15 divided by (x-1)?

Answer 9

correct. Use synthetic division. If you are not familiar with it do long division. You can learn both methods by typing: polynomial synthetic division in YouTube. With video it is much easier to teach and learn than typing all those division symbols and aligning numbers here.

Answer 10

Thank you very much for the information, I'll make sure to do that right away.

Answer 11

You are welcome.

Try this: https://www.youtube.com/watch?v=lLgRS0mUZLw

Answer 12

Another excellent video: https://www.youtube.com/watch?v=bZoMz1Cy1T4

Answer 13

Okay now that I've found the linear factor how would i find which linear factor denotes the length of 13 feet?

Answer 14

What are your linear factors?

Answer 15

2x^2+11+15 is what I got after I watched the first video

Answer 16

This is what my assignment asks now

Which linear factor denotes the length of 13 feet? In feet, what are the length, width, and height of the box? Calculate the volume based upon your findings. Solve for x and substitute your answer

Answer 17

The middle term should be 11x (not just 11).
Now you have to factor 2x^2 + 11x +15. This is a quadratic. You can use the AC method where you multiply the the first coefficient and the constant: 2 * 15 = 30. Write various factors of 30 and see which two factors add to the middle coefficient of 11.

Answer 18

Yeah that's is what I meant sorry my keyboard isn't working well. Alright I'll do that.

Answer 19

So I ended up with x=-6 and x=-5

Answer 20

We need to factor 2x^2 + 11x +15
AC method: 2 * 15 = 30
Factors of 30:
1 and 30
2 and 15
3 and 10
5 and 6
Out of these four choices, 5 and 6 add to the middle coefficient 11.
So we write 2x^2 + 11x +15 as
2x^2 + 6x + 5x +15 =
2x(x + 3) + 5(x + 3) =
(2x + 5)(x + 3)

The original polynomial 2x^3+9x^2+4x-15 = (2x+5)(x+3)(x-1)

Answer 21

that's what i got originally but then i got confused and thought i did it wrong.

Answer 22

So now what do I do?

Answer 23

2x^3+9x^2+4x-15 = (2x+5)(x+3)(x-1)
The polynomial represent Volume of the box.
We know volume of a box is length x width x height
We have factored the polynomial into: (2x+5) * (x+3) * (x-1)
So one factor is length, one factor is width and one factor is height. But which is which? In the problem they say: "The box is (x-1) feet from lid to base." This implies, (x-1) is height. So we have to decide which is length? (2x+5) or (x+3). Which one do you think it is?

Answer 24

(2x+5)?

Answer 25

Correct! Normally we refer to the longer side as the length and the shorter side as the width. Out of (2x+5) and (x+3), (2x+5) is bigger than (x+3) for positive x.
So length is (2x+5), width is (x+3) and height is (x-1).

Answer 26

We are told the length is 13 feet.
length = 2x + 5 = 13
solve for x.
put x back and find width and height.
multiply the 3 numbers and find the volume.

Answer 27

so height is 3, length obviously is 13 and width is 7?

Answer 28

correct. Add the units feet to each.
multiply the three numbers to get volume and the unit is cubic feet or feet^3.

Answer 29

I have one last question

Answer 30

go ahead

Answer 31

Using the graphing calculator, analyze the graph. What is the relationship between the graph and the linear factors of the polynomial, ?

Answer 32

I'm not sure how to go aboout this

Answer 33

Volume = 2x^3+9x^2+4x-15 = (2x+5)(x+3)(x-1)
If you plot the graph of the volume (the polynomial), you will notice the volume becomes zero when the graph crosses the x axis. What values of x will make the volume zero? When any of the factors is zero, the volume will be zero.
(2x+5)(x+3)(x-1) is zero when 2x + 5 = 0 or x + 3 = 0 or x - 1 = 0
2x + 5 = 0. x = -2.5
x + 3 = 0. x = -3
x - 1 = 0. x = 1

The graph will cross the x axis at x = -3, -2.5 and 1.

Answer 34

So the relationship between the graph and the linear factors of the polynomial is the graph crosses the x axis at those points where each of the linear factor becomes zero.

Answer 35

Wow, thank you so much, you were super helpful and I learned a lot.

Answer 36

You are welcome.