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

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 – 2t² – 9t – 12

Remainder is 0 hence t² -3 is a factor of 2t² + 3t² – 2t² – 9t – 12

(ii)        x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

(3)       x³ – 3x + 1, x⁵ – 4x³ + x² + 3x + 1

Remainder is 2 so x² – 3x + 1 is not a factor