Question

A polynomial function has a zero at 4 (multiplicity 3) and 0 (multiplicity 1). Write a function in standard form that can represent this function.

Answer 1

Answer:

(x^4) - 64x

Step-by-step explanation:

zeros at 4 and 0 are the roots so can be factor as x*(x-4) and the multiplicity tels to what power you have to raise those factors

$x^{1} *(x-4)^{3}$ becuase multiplicity of 1 for root at 0, and multiplicity of 3 at root 4

now to write this in standard form

$x*(x-4)^{3} = \\x*(x-4)(x^{2} +4x+16)= \\(x^{2} -4x)(x^{2} +4x+16) = \\x^{4} +4x^{3} +16x^{2} -4x^{3} -16x^{2} -64x = \\x^{4} -64x$