Question

Find a polynomial function of degree 4 with -4 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.

Answer 1

Answer:

  p(x) = x⁴ +12x³ +48x² +64x

Step-by-step explanation:

If -4 is a zero, then (x -(-4)) = (x +4) is a factor. If its multiplicity is 3, then it is a factor 3 times. The other factor is (x-0) = x, so the function is ...

  p(x) = x(x +4)³

Expanding gives ...

  p(x) = x⁴ +12x³ +48x² +64x