Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

(i)


(ii)


(iii)



(i) t2-3 = t2+0t-3



Since the remainder is 0,


Hence, t2 – 3 is a factor of 2t4+3t3-2t2-9t-12.


(ii)



Since the remainder is 0,


Hence, x2+3x+1 is a factor of 3x4+5x3-7x2+2x+2.


(iii)



Since the remainder ≠0,


Hence, x3-3x+1 is not a factor of x5-4x3+ x2+3x+1.


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