Question #45160

1 Answer
Feb 13, 2017

Answer:

See explanation.

Explanation:

To solve this task you need to use the folloing feature of polynomial:

If #a# is a zero of polynomial with multiplicity #n#, then the polynomial is divisible by #(x-a)^n# and not divisible by #(x-a)^(n+1)#

As stated above the polynomial would have to be divisible by #(x-3)^3#, and #(x-0)^2#. The only polynomial of degree #5# fulfilling theses conditions is:

#P(x)=(x-3)^3*x^2=(x^3+3x^2+3x+1)*x^2#
#=x^5+3x^4+3x^3+x^2#