(i) x + 1, 2x2 + 5x + 4
Quotient: 2x + 3
Remainder: 1
Since remainder is 1 therefore the first polynomial is NOT a factor of the second polynomial.
(ii) y - 2, 3y3 + 5y2 + 5y + 2
Quotient: 3y2 + 11y + 27
Remainder: 56
Since remainder is 56 therefore the first polynomial is NOT a factor of the second polynomial.
(iii) 4x2 - 5, 4x4 + 7x2 + 15
Quotient: x2 + 3
Remainder: 30
Since remainder is 30 therefore the first polynomial is NOT a factor of the second polynomial.
(iv) 4 - z, 3z2 - 13z + 4
Quotient: -3z + 1
Remainder: 0
Since remainder is 0 therefore the first polynomial is a factor of the second polynomial.
(v) 2a - 3, 10a2 - 9a - 5
Quotient: 5a + 3
Remainder: 4
Since remainder is 4 therefore the first polynomial is NOT a factor of the second polynomial.
(vi) 4y + 1, 8y2 - 2y + 1
Quotient: 2y - 1
Remainder: 2
Since remainder is 2 therefore the first polynomial is NOT a factor of the second polynomial.