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

Question

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: (i) (ii) (iii)

Philoid · Accepted Answer

(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.