What are the zeroes of the function? What are their multiplicities?

f(x) = x^4 – 4x^3 + 3x^2

a. The numbers –1 and –3 are zeroes of multiplicity 2; the number 0 is a zero of multiplicity 1.
b. The number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeroes of multiplicity 1.
c. The numbers 0 and 1 are zeroes of multiplicity 2; the number 3 is a zero of multiplicity 1.
d. The number 0 is a zero of multiplicity 2; the numbers –1 and –3 are zeroes of multiplicity 1.

please help me understand how to do this

Question

What are the zeroes of the function? What are their multiplicities?

f(x) = x^4 – 4x^3 + 3x^2 


a. The numbers –1 and –3 are zeroes of multiplicity 2; the number 0 is a zero of multiplicity 1.
b. The number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeroes of multiplicity 1.
c. The numbers 0 and 1 are zeroes of multiplicity 2; the number 3 is a zero of multiplicity 1.
d. The number 0 is a zero of multiplicity 2; the numbers –1 and –3 are zeroes of multiplicity 1.

please help me understand how to do this

amistre64 · Answer

you can either factor or synthetic divide the original to work out its zeros; or you can plug in the numbers given to see if they zero it out

amistre64 · Answer

or you can try a ferrari method which sounds fast but takes forever

amistre64 · Answer

factoring is prolly the easiest to determine tho