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What is the sum of the squares of the coefficients of $4(x^4 + 3x^2 + 1)$?

michaelcai  Sep 11, 2017

Best Answer 

 #1
avatar+4491 
+2

4(x4 + 3x2 + 1)  =  4x4 + 12x2 + 4

 

As best I can tell, the  "4"  at the end is not considered a coefficient.

So....the coefficients are just  4  and  12 .

 

The sum of the squares of  4  and  12  =  42 + 122  =  16 + 144  =  160

hectictar  Sep 11, 2017
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4+0 Answers

 #1
avatar+4491 
+2
Best Answer

4(x4 + 3x2 + 1)  =  4x4 + 12x2 + 4

 

As best I can tell, the  "4"  at the end is not considered a coefficient.

So....the coefficients are just  4  and  12 .

 

The sum of the squares of  4  and  12  =  42 + 122  =  16 + 144  =  160

hectictar  Sep 11, 2017
 #2
avatar+201 
+1

yeah, I got 160 as well, but my answer checking thing says its incorrect...

michaelcai  Sep 11, 2017
 #3
avatar+4491 
+1

Hmmm...maybe the 4 at the end is considered a coefficient. It's a coefficient of x0 .

 

If that's the case... then the answer        =  42 + 122 + 42  =  16 + 144 + 16  =  176

 

Does it say that's the right answer? I'm curious now....

hectictar  Sep 12, 2017
 #4
avatar+1125 
+1

No, 4 is NOT a coefficient. 4, in this biquadratic expression (fancy name for a quartic expression that excludes terms with an odd degree and is written in the form \(ax^4+cx^2+e\)) is a constant. 

 

Remember that coefficients are numbers that multiply a variable. There is no variable that alongside the number 4, so it is a plain and boring constant.

TheXSquaredFactor  Sep 13, 2017

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