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# 1: There is a polynomial which, when multiplied by x^2 + 2x + 3, gives 2x^5 + 3x^4 + 8x^3 + 8x^2 + 18x + 9. What is that polynomial?

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+771

1: There is a polynomial which, when multiplied by x^2 + 2x + 3, gives 2x^5 + 3x^4 + 8x^3 + 8x^2 + 18x + 9. What is that polynomial?

2:  What is the coefficient of x in (x^4 + x^3 + x^2 + x + 1)^4?

3:  What is the coefficient of x^3 in this expression? [(x^4 + x^3 + x^2 + x + 1)^4]

Thanks!

AnonymousConfusedGuy  Nov 28, 2017
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#1
+83955
+3

x^2 + 2x + 3

2x^5 + 3x^4 + 8x^3 + 8x^2 + 18x + 9

We can determine this by polynomial division

2x^3    -   x^2      +    4x       + 3

x^2  +  2x  +  3  [   2x^5    +   3x^4    +    8x^3   +  8x^2  +   18x   +  9  ]

2x^5    +  4x^4    +    6x^3

__________________________________

- x^4      +    2x^3     +    8x^2

-x^4      -      2x^3     -     3x^2

_________________________

4x^3    +  11x^2    +  18x

4x^3    +    8x^2    +  12x

__________________________

3x^2   +  6x      +  9

3x^2   +  6x      +  9

_________________

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The answer is shown in red

CPhill  Nov 28, 2017
#2
+771
+2

Hey thanks man!

AnonymousConfusedGuy  Nov 28, 2017
#3
+1

This is the expanded form of:   (x^4 + x^3 + x^2 + x + 1)^4?
x^16 + 4 x^15 + 10 x^14 + 20 x^13 + 35 x^12 + 52 x^11 + 68 x^10 + 80 x^9 + 85 x^8 + 80 x^7 + 68 x^6 + 52 x^5 + 35 x^4 + 20 x^3 + 10 x^2 + 4 x + 1

2)  What is the 16th term in the expansion of  (x^4 + x^3 + x^2 + x + 1)^4?
=4x
3) What is the 14th term in the expansion of  (x^4 + x^3 + x^2 + x + 1)^4?
=20x^3

Guest Nov 28, 2017

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