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Write the polynomial as the product of linear factors and list all the zeros of the function. h(x) = x^3 – 3x^2 + 4x – 2

## Answer

The constant term of the given function is -2 and its factors are +-2 and +-1.

The leading coefficient of the given function is 1 and its factors are +-1.

By dividing factors of the constant term by factors of the leading coefficient, we get the possible rational zeros. Therefore, possible rational zeros are +-2 and +-1.

Let us use the synthetic division to show that x = 1 is a zero of x^3 – 3x^2 + 4x – 2:

We got x^2 – 2x + 2 and the remainder of 0. Therefore x = 1 is a zero of the given function.

Let us use the quadratic formula to find the zeros of x^2 – 2x + 2. We have a = 1, b = -2 and c = 2.

THe factored function is h(x) = (x-1)(x-1-i)(x-1+i).

Zeros of the given function are x =1 and x = 1 +-i.

Zeros of the function h(x) = (x-1)(x-1-i)(x-1+i) are x = 1 and x = 1+-i.