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What is the coefficient of x^3 when

24x^4+6x^3+4x^2-7x-5

is multiplied by

6x^3+3x^2+3x+4

and the like terms are combined?

 Dec 28, 2018
 #1
avatar+3729 
+2

As you can see, just distribute as these range by increasing power. The answer should be -15. \(144x^7+108x^6+114x^5+84x^4\boxed{-15}x^3-20x^2-43x-20\)

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 Dec 28, 2018
 #3
avatar+534 
+2

Yay, our answers agree!

CoolStuffYT  Dec 28, 2018
 #2
avatar+534 
+2

We want the \(x^3\) coefficient of:

 

(\(24x^4+6x^3+4x^2-7x-5)(6x^3+3x^2+3x+4)\)

We see that the only ways of this is \(x^3*x^0, x^2*x^1\) .

Therefore, knock out the \(24x^4\) .

Now pair some numbers: \(6x^3\times 4, 4x^2\times 3x, -7x \times 3x^2, -5 \times 6x^3\)

Expanding, we get \(24x^3+12x^3-21x^3-30x^3=3x^3-18x^3=-15x^3\)

Therefore, the coefficient of \(x^3\) is -15.

 

You are very welcome!

:P

 Dec 28, 2018

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