Function notation help again!!
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Function notation help again!!

[From: ] [author: ] [Date: 11-09-08] [Hit: ]
all the x^2 to each other etc.Do not mix the different powers together.21x^3 + 9x^2 + 35 x^2 + 15x = 21x^3 + 44x^2 + 15x-f(x)g(x) means to multiply your two functions together.Multiply out the brackets, collect any like terms, and youre done.......
Im having such a hard time with these problems I really need a good detailed answer, I'm really trying so please dont think I want this community to do all my homework, I really want to learn!

given f(x)=3x^2 + 5x and g(x)=7x+3 find f(x)g(x)

thanks!

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This is asking you to multiply the two functions together. This is like multiplying a polynomial.

Write out f(x)g(x) using the part on the right hand sides of the equations:

(3x^2 + 5x) * (7x+3) =

Now use that FOIL method of multiplying
First: Multiply the 3x^2 times 7x
Outside: Multiply 3x^2 times 3
Inside: Multiply 5x times 7x
Last: 5x times 3

If there were minus signs in front of any of the coefficients, you need to include that sign when multiplying.

Now add all these parts together

(3x^2 + 5x) * (7x+3) = 21x^3 + 9x^2 + 35 x^2 + 15x
First + Outside + Inside + Last

Now add the things that have the same powers on the variable all the x^3 to each other, all the x^2 to each other etc. Do not mix the different powers together.

21x^3 + 9x^2 + 35 x^2 + 15x = 21x^3 + 44x^2 + 15x

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f(x)g(x) means to multiply your two functions together. So

f(x)g(x) = (3x^2 + 5x )(7x+3)

Multiply out the brackets, collect any like terms, and you're done.
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