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Question

Check in which case the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
$t^2-3, 2t^4+3t^3-2t^2-9t-12$

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Solution

t23,2t4+3l:t32t29t12Fist polynomial is t2
Second Polynomial is
24+3t32t29t12Let us divide
2t4+3t32t29t12 by t23
t23)2t4+3t32t29t12(2t2+3t+42t4+06t2- + - ..........
3t3+4t29t12
3t3+09t- + -
...............
4t2+012
4t2+012............
0The remainder is zero , therefore t23 is a factor of 2t4+3t32t29t12



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