Question

Help with algebra 2 please

Answer 1

wo Martians, Splott and Fizzle, invite you to pilot their giant robot. The heat generated by one leg mechanism is represented by the function f(x) = 3x2 + 20. The heat generated by one arm mechanism is represented by g(x) = 3x2 + 4x - 5. Describe to Splott and Fizzle, using complete sentences, which of the operations, addition, subtraction, multiplication, and division, will result in the largest degree function, and which operation will result in the smallest degree function.

Answer 2

(fg)(x) = (3x^2 + 20)(3x^2 + 4x - 5)
Use FOIL
9x^4 + 12x^3 - 15x^2 + 60x^2 + 80x - 100
Combine like terms
9x^4 + 12x^3 + 45x^2 + 80x - 100

Answer 3

^That is what I have for multiplication. I'm not sure what to do next (if anything) for that.

Answer 4

alg 2 is easy try calculus

Answer 5

Haha, no I'm good. Can you help me with it? Please :D

Answer 6

one thing to try is using an online algebraic calculator

Answer 7

I've tried mathway and wolframalpha, but neither show you the steps unless you pay. @TBNRfrags

Answer 8

http://www.algebrahelp.com/calculators/equation/ try this its awesome and 100%free

Answer 9

It gave me an error when I put (f/g)(x) = (3x^2 + 20)/(3x^2 + 4x - 5)

Answer 10

@ganeshie8 , @agent0smith

Answer 11

@AkashdeepDeb If you could help me I would appreciate it so much. I've been stuck on this for hours (not exaggerating).

Answer 12

Do you know what a degree of a function is?

Answer 13

A function's degree is basically the largest power of the domain or 'x'.

Let us say, f(x) = x^4 + x^2 + 35
Then the degree of this function is 4. Because it is the greatest power of x.

Answer 14

Yeah

Answer 15

Now basically to get the largest degree function you should multiply.
Because let us say you multiply

f(x) = x+1 [degree is 1]
g(x) = x+2 [degree is 2]

(f*g) (x) = (x+1)(x+2) = x2 + 3x + 2 [degree is 2]

Which is greater than the degree of the original functions.
So multiply to get the function with the highest degree.

If you added, you would get the same degree because x's power would be the same. and the same case would have been for subtraction as well.

Answer 16

Okay, is the multiplication that I did above correct?

Answer 17

Yes.

Answer 18

Now what do you think can be done for lowest degree?

Answer 19

Division. Would it be (f/g)(x) = (3x^2 + 20) / (3x^2 + 4x - 5)?

Answer 20

Yes, excellent! You need to divide 2 functions, where the degree of the numerator should be greater than the degree of the denominator to get a function with a less degree.

Answer 21

Okay, how do I do that? lol

Answer 22

The question does not ask you to do that! But even if you want to, then you need to write the numerator as 3x2 + 0x + 20 and use the process of long division of polynomials!

Answer 23

Oh okay. It says to describe it, so what would I put?

Answer 24

I can teach you long division but I don't think you require it. I don't know what you should put in your answer. Do you need an explanation?

Try to understand what's happening here.

To get the highest power, we multiply, why?
Because when we multiply we affect the power of the 'x' in the equation, you may know if 'x' is multiplied to 'x' it results in x^2 and so, we multiply to get a higher degree.

To get the lowest power, we divide, why?
Because when we divide we directly reduce the power of the polynomial/function [almost the same], say for example we are dividing (x+1)^3/(x+1) = (x+1)^2, thus the result has a lesser degree. Whereas when functions of equal degrees are divided you ought to get a lesser degree equation.

Answer 25

They don't teach long division until the next module, so I'm not going to worry about it. Thanks a lot for all of your time and help. I really appreciate it.