Question

Write the polynomial as the product of linear factors.
h(x) = x3 − 6x2 + 13x − 10

Answer 1

h(x) = (x -2)(x -2+i)(x -2-i)

Explanation:

You want the linear factorization of h(x) = x³ -6x² +13x -10.

Factors

A graphing calculator (attachment 2) shows the one positive real root is x = 2. This means (x-2) is a factor.

When we factor that out, we have a quadratic with no real roots. The vertex of its graph at (2, 1) tells us the roots of it are 2±√-1 = 2±i.

Each root p gives rise to a linear factor (x -p), so the factorization is ...

h(x) = (x -2)(x -2+i)(x -2-i)

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Additional comment

The first attachment shows these factors multiply out to give the polynomial h(x).

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