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Answer 1 · 2016-10-31T00:40:59

#f(x)=x^3-4x^2+5x-2#

If the zero is #a# and the multiplicity is #b#, then a factor of the polynomial will be #(x-a)^b#.

The factor for a zero of #2# and multiplicity #1# is #(x-2)^1#.

The factor for a zero of #1# and multiplicity #2# is #(x-1)^2#.

The polynomial is the product of the factors.

#f(x)=(x-2)^1(x-1)^2#.

Note: the sum of the exponents is #3#, which means the degree is #3#.

Rewriting:

#f(x)=(x-2)(x-1)(x-1)#

Multiplying #(x-1)(x-1)#

#f(x)=(x-2)(x^2-2x+1)#

Multiplying by #(x-2)#

#f(x)=x^3-2x^2+x-2x^2+4x-2#

Combining like terms#

#f(x)=x^3-4x^2+5x-2#