Question

Question #ed07b

Answer 1

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

Explanation:

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`