15. What are the quotient and remainder, when 3x^4+5x^3-7x^2+2x+2 is divided by x^2+3x+1 ?
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Given f(x) = 3x^4 + 5x^3 - 7x^2 + 2x + 2.
Given g(x) =x^2 + 3x + 1.
Now, divide f(x) by g(x), we get
3x^2 - 4x + 2
-------------------------------------------------------
x^2 + 3x + 1) 3x^4 + 5x^3 - 7x^2 + 2x + 2
3x^4 + 9x^3 + 3x^2
-------------------------------------------------------------
-4x^3 - 10x^2 + 2x + 2
-4x^3 - 12x^2 - 4x
------------------------------------------------------------------
2x^2 + 6x + 2
2x^2 + 6x + 2
---------------------------------------------------------------------
0.
Therefore, Quotient = 3x^2 - 4x + 2, remainder = 0.
Hope this helps!
Given g(x) =x^2 + 3x + 1.
Now, divide f(x) by g(x), we get
3x^2 - 4x + 2
-------------------------------------------------------
x^2 + 3x + 1) 3x^4 + 5x^3 - 7x^2 + 2x + 2
3x^4 + 9x^3 + 3x^2
-------------------------------------------------------------
-4x^3 - 10x^2 + 2x + 2
-4x^3 - 12x^2 - 4x
------------------------------------------------------------------
2x^2 + 6x + 2
2x^2 + 6x + 2
---------------------------------------------------------------------
0.
Therefore, Quotient = 3x^2 - 4x + 2, remainder = 0.
Hope this helps!
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