+1452 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!
+129907 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
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- x^4 + 2x^3 + 8x^2
-x^4 - 2x^3 - 3x^2
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4x^3 + 11x^2 + 18x
4x^3 + 8x^2 + 12x
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3x^2 + 6x + 9
3x^2 + 6x + 9
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0
The answer is shown in red
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
