Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
(i) t²−3, 2t⁴+3t³−2
(ii) x²+3x+1, 3x⁴+5x³−7x²+2x+2
(iii) x³−3x+1, x⁵−4x³+x²+3x+1

(i) Given polynomials
t²−3, 2t⁴+3t³−2
Division of 2t⁴+3t³−2 by t²−3
Remainder is 0, hence t²−3 is a factor of 2t⁴+3t³−2
(ii) Given
x²+3x+1, 3x⁴+5x³−7x²+2x+2
Division of 3x⁴+5x³−7x²+2x+2 by x²+3x+1 is
Remainder is 0, hence x²+3x+1 is a factor of 3x⁴+5x³−7x²+2x+2
(iii) x³−3x+1, x⁵−4x³+x²+3x+1
Division of x⁵−4x³+x²+3x+1 by x³−3x+1 is
Remainder is 2, hence x³−3x+1 is not a factor of x⁵−4x³+x²+3x+1