Applying the Division Algorithm, check whether the first polynomial is a factor of the second polynomial:

t² – 5t + 6,t² + 11t – 6

Applying the Division Algorithm, check whether the first polynomial is a factor of the second polynomial:

x² – 4x + 3,x³ – x³ – 3x⁴ – x + 3

Applying the Division Algorithm, check whether the first polynomial is a factor of the second polynomial:

t – 1, t³ + t² – 2t + 1

Give examples of polynomials p(x), g(x), q(x) and r(x) satisfying the Division Algorithm

p(x) = g(x).q(x) + r(x),deg r(x)<deg g(x)

And also satisfying

(i) deg p(x) = deg q(x) + 1

(ii)deg q(x) = 1

(iii) deg q(x) = deg r(x) + 1

Find all the zeroes of the polynomial given below having given numbers as its zeroes.

x³ – 6x² + 11x – 6;3