Form a polynomial whose zeros and degree are given zeros 1 m

Form a polynomial whose zeros and degree are given. zeros: 1, multiplicity 1; 4, multiplicity 2; degree 3

Solution

zeros: x=1, multiplicity 1; -----(x-1)

zeros x=4, multiplicity 2-----( x-4)^2

3rd degree polynomial : f(x) = (x-1)(x-4)^2

= (x-1)( x^2 + 16 -8x)

= x^3 +16x -8x^2 -x^2 -16 +8x)

=x^3 - 9x^2 +24x -16